CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Signal processing - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )enwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy", "wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"c3a46cb9-b673-4677-ac31-26014c45d5ab","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Signal_processing","wgTitle":"Signal processing","wgCurRevisionId":1258826289,"wgRevisionId":1258826289,"wgArticleId":29324,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Articles with short description","Short description is different from Wikidata","Articles lacking in-text citations from January 2017","All articles lacking in-text citations","Articles needing cleanup from June 2017","All pages needing cleanup","Articles with sections that need to be turned into prose from June 2017","Articles with multiple maintenance issues","Signal processing","Mass media technology","Telecommunication theory"],"wgPageViewLanguage":"en", "wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Signal_processing","wgRelevantArticleId":29324,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":false,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":20000,"wgRelatedArticlesCompat":[],"wgCentralAuthMobileDomain":false,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q208163", "wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.makeCollapsible.styles":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.media","site","mediawiki.page.ready","jquery.makeCollapsible","mediawiki.toc", "skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.ReferenceTooltips","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=en&modules=ext.cite.styles%7Cext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.4"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/1/11/Cosine_Series_Plus_Noise.png"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="900"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/1/11/Cosine_Series_Plus_Noise.png/800px-Cosine_Series_Plus_Noise.png"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="600"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/thumb/1/11/Cosine_Series_Plus_Noise.png/640px-Cosine_Series_Plus_Noise.png"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="480"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Signal processing - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//en.m.wikipedia.org/wiki/Signal_processing"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Signal_processing&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (en)"> <link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://en.wikipedia.org/wiki/Signal_processing"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Signal_processing rootpage-Signal_processing skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Jump to content</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Main menu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Main menu</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia"><span>Contents</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events"><span>Current events</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x"><span>Random article</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works"><span>About Wikipedia</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia"><span>Contact us</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia"><span>Help</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia"><span>Learn to edit</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors"><span>Community portal</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia"><span>Upload file</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Appearance" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Appearance</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en" class=""><span>Donate</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:CreateAccount&returnto=Signal+processing" title="You are encouraged to create an account and log in; however, it is not mandatory" class=""><span>Create account</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:UserLogin&returnto=Signal+processing" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class=""><span>Log in</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Log in and more options" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personal tools" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personal tools</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en"><span>Donate</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=Signal+processing" title="You are encouraged to create an account and log in; however, it is not mandatory"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Create account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=Signal+processing" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log in</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing"><span>learn more</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contents" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Definition_of_a_signal" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Definition_of_a_signal"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Definition of a signal</span> </div> </a> <ul id="toc-Definition_of_a_signal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Categories" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Categories"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Categories</span> </div> </a> <button aria-controls="toc-Categories-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Categories subsection</span> </button> <ul id="toc-Categories-sublist" class="vector-toc-list"> <li id="toc-Analog" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Analog"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Analog</span> </div> </a> <ul id="toc-Analog-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Continuous_time" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Continuous_time"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Continuous time</span> </div> </a> <ul id="toc-Continuous_time-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Discrete_time" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Discrete_time"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Discrete time</span> </div> </a> <ul id="toc-Discrete_time-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Digital" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Digital"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Digital</span> </div> </a> <ul id="toc-Digital-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Nonlinear" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Nonlinear"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Nonlinear</span> </div> </a> <ul id="toc-Nonlinear-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Statistical" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Statistical"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6</span> <span>Statistical</span> </div> </a> <ul id="toc-Statistical-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Application_fields" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Application_fields"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Application fields</span> </div> </a> <ul id="toc-Application_fields-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Typical_devices" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Typical_devices"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Typical devices</span> </div> </a> <ul id="toc-Typical_devices-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Mathematical_methods_applied" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mathematical_methods_applied"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Mathematical methods applied</span> </div> </a> <ul id="toc-Mathematical_methods_applied-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Signal processing</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 48 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-48" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">48 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Seinverwerking" title="Seinverwerking – Afrikaans" lang="af" hreflang="af" data-title="Seinverwerking" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%B9%D8%A7%D9%84%D8%AC%D8%A9_%D8%A7%D9%84%D8%A5%D8%B4%D8%A7%D8%B1%D8%A9" title="معالجة الإشارة – Arabic" lang="ar" hreflang="ar" data-title="معالجة الإشارة" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Procesamientu_de_se%C3%B1ales" title="Procesamientu de señales – Asturian" lang="ast" hreflang="ast" data-title="Procesamientu de señales" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%82%E0%A6%95%E0%A7%87%E0%A6%A4_%E0%A6%AA%E0%A7%8D%E0%A6%B0%E0%A6%95%E0%A7%8D%E0%A6%B0%E0%A6%BF%E0%A6%AF%E0%A6%BC%E0%A6%BE%E0%A6%9C%E0%A6%BE%E0%A6%A4%E0%A6%95%E0%A6%B0%E0%A6%A3" title="সংকেত প্রক্রিয়াজাতকরণ – Bangla" lang="bn" hreflang="bn" data-title="সংকেত প্রক্রিয়াজাতকরণ" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9E%D0%B1%D1%80%D0%B0%D0%B1%D0%BE%D1%82%D0%BA%D0%B0_%D0%BD%D0%B0_%D1%81%D0%B8%D0%B3%D0%BD%D0%B0%D0%BB%D0%B8" title="Обработка на сигнали – Bulgarian" lang="bg" hreflang="bg" data-title="Обработка на сигнали" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Processament_de_senyals" title="Processament de senyals – Catalan" lang="ca" hreflang="ca" data-title="Processament de senyals" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A1%D0%B8%D0%B3%D0%BD%D0%B0%D0%BB%D1%81%D0%B5%D0%BD%D0%B5_%D1%82%D0%B8%D1%80%D0%BF%D0%B5%D0%B9%D0%BB%D0%B5%D0%BD%D0%B8" title="Сигналсене тирпейлени – Chuvash" lang="cv" hreflang="cv" data-title="Сигналсене тирпейлени" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Zpracov%C3%A1n%C3%AD_sign%C3%A1lu" title="Zpracování signálu – Czech" lang="cs" hreflang="cs" data-title="Zpracování signálu" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Signalbehandling" title="Signalbehandling – Danish" lang="da" hreflang="da" data-title="Signalbehandling" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Signalverarbeitung" title="Signalverarbeitung – German" lang="de" hreflang="de" data-title="Signalverarbeitung" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Signaalit%C3%B6%C3%B6tlus" title="Signaalitöötlus – Estonian" lang="et" hreflang="et" data-title="Signaalitöötlus" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CF%80%CE%B5%CE%BE%CE%B5%CF%81%CE%B3%CE%B1%CF%83%CE%AF%CE%B1_%CF%83%CE%AE%CE%BC%CE%B1%CF%84%CE%BF%CF%82" title="Επεξεργασία σήματος – Greek" lang="el" hreflang="el" data-title="Επεξεργασία σήματος" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Procesado_de_se%C3%B1al" title="Procesado de señal – Spanish" lang="es" hreflang="es" data-title="Procesado de señal" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Signal-prilaborado" title="Signal-prilaborado – Esperanto" lang="eo" hreflang="eo" data-title="Signal-prilaborado" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Seinale_prozesamendu" title="Seinale prozesamendu – Basque" lang="eu" hreflang="eu" data-title="Seinale prozesamendu" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%BE%D8%B1%D8%AF%D8%A7%D8%B2%D8%B4_%D8%B3%DB%8C%DA%AF%D9%86%D8%A7%D9%84" title="پردازش سیگنال – Persian" lang="fa" hreflang="fa" data-title="پردازش سیگنال" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Traitement_du_signal" title="Traitement du signal – French" lang="fr" hreflang="fr" data-title="Traitement du signal" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%8B%A0%ED%98%B8_%EC%B2%98%EB%A6%AC" title="신호 처리 – Korean" lang="ko" hreflang="ko" data-title="신호 처리" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%95%E0%A5%87%E0%A4%A4_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%B8%E0%A4%82%E0%A4%B8%E0%A5%8D%E0%A4%95%E0%A4%B0%E0%A4%A3" title="संकेत प्रसंस्करण – Hindi" lang="hi" hreflang="hi" data-title="संकेत प्रसंस्करण" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Pengolahan_sinyal" title="Pengolahan sinyal – Indonesian" lang="id" hreflang="id" data-title="Pengolahan sinyal" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Ukudludlungwa_kwesiyabizo" title="Ukudludlungwa kwesiyabizo – Zulu" lang="zu" hreflang="zu" data-title="Ukudludlungwa kwesiyabizo" data-language-autonym="IsiZulu" data-language-local-name="Zulu" class="interlanguage-link-target"><span>IsiZulu</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A2%D7%99%D7%91%D7%95%D7%93_%D7%90%D7%95%D7%AA%D7%95%D7%AA" title="עיבוד אותות – Hebrew" lang="he" hreflang="he" data-title="עיבוד אותות" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9E%D0%B1%D1%80%D0%B0%D0%B1%D0%BE%D1%82%D0%BA%D0%B0_%D0%BD%D0%B0_%D1%81%D0%B8%D0%B3%D0%BD%D0%B0%D0%BB" title="Обработка на сигнал – Macedonian" lang="mk" hreflang="mk" data-title="Обработка на сигнал" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Pemprosesan_isyarat" title="Pemprosesan isyarat – Malay" lang="ms" hreflang="ms" data-title="Pemprosesan isyarat" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%86%E1%80%85%E1%80%BA%E1%80%82%E1%80%94%E1%80%9A%E1%80%BA%E1%80%9E%E1%80%81%E1%80%BC%E1%80%84%E1%80%BA%E1%80%B8" title="ဆစ်ဂနယ်သခြင်း – Burmese" lang="my" hreflang="my" data-title="ဆစ်ဂနယ်သခြင်း" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Signaalverwerking" title="Signaalverwerking – Dutch" lang="nl" hreflang="nl" data-title="Signaalverwerking" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%BF%A1%E5%8F%B7%E5%87%A6%E7%90%86" title="信号処理 – Japanese" lang="ja" hreflang="ja" data-title="信号処理" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Signalbehandling" title="Signalbehandling – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Signalbehandling" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Signalhandsaming" title="Signalhandsaming – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Signalhandsaming" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Przetwarzanie_sygna%C5%82%C3%B3w" title="Przetwarzanie sygnałów – Polish" lang="pl" hreflang="pl" data-title="Przetwarzanie sygnałów" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Processamento_de_sinal" title="Processamento de sinal – Portuguese" lang="pt" hreflang="pt" data-title="Processamento de sinal" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Procesarea_semnalelor" title="Procesarea semnalelor – Romanian" lang="ro" hreflang="ro" data-title="Procesarea semnalelor" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9E%D0%B1%D1%80%D0%B0%D0%B1%D0%BE%D1%82%D0%BA%D0%B0_%D1%81%D0%B8%D0%B3%D0%BD%D0%B0%D0%BB%D0%BE%D0%B2" title="Обработка сигналов – Russian" lang="ru" hreflang="ru" data-title="Обработка сигналов" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%83%E0%B6%82%E0%B6%A5%E0%B7%8F_%E0%B7%83%E0%B7%90%E0%B6%9A%E0%B7%83%E0%B7%94%E0%B6%B8" title="සංඥා සැකසුම – Sinhala" lang="si" hreflang="si" data-title="සංඥා සැකසුම" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Signal_processing" title="Signal processing – Simple English" lang="en-simple" hreflang="en-simple" data-title="Signal processing" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Obdelava_signalov" title="Obdelava signalov – Slovenian" lang="sl" hreflang="sl" data-title="Obdelava signalov" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9E%D0%B1%D1%80%D0%B0%D0%B4%D0%B0_%D1%81%D0%B8%D0%B3%D0%BD%D0%B0%D0%BB%D0%B0" title="Обрада сигнала – Serbian" lang="sr" hreflang="sr" data-title="Обрада сигнала" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Pamros%C3%A9san_sinyal" title="Pamrosésan sinyal – Sundanese" lang="su" hreflang="su" data-title="Pamrosésan sinyal" data-language-autonym="Sunda" data-language-local-name="Sundanese" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Signalbehandling" title="Signalbehandling – Swedish" lang="sv" hreflang="sv" data-title="Signalbehandling" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AF%81%E0%AE%B1%E0%AE%BF%E0%AE%95%E0%AF%88%E0%AE%9A%E0%AF%8D_%E0%AE%9A%E0%AF%86%E0%AE%AF%E0%AE%B2%E0%AE%BE%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%AE%E0%AF%8D" title="குறிகைச் செயலாக்கம் – Tamil" lang="ta" hreflang="ta" data-title="குறிகைச் செயலாக்கம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%9B%E0%B8%A3%E0%B8%B0%E0%B8%A1%E0%B8%A7%E0%B8%A5%E0%B8%9C%E0%B8%A5%E0%B8%AA%E0%B8%B1%E0%B8%8D%E0%B8%8D%E0%B8%B2%E0%B8%93" title="การประมวลผลสัญญาณ – Thai" lang="th" hreflang="th" data-title="การประมวลผลสัญญาณ" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Sinyal_i%C5%9Fleme" title="Sinyal işleme – Turkish" lang="tr" hreflang="tr" data-title="Sinyal işleme" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9E%D0%B1%D1%80%D0%BE%D0%B1%D0%BA%D0%B0_%D1%81%D0%B8%D0%B3%D0%BD%D0%B0%D0%BB%D1%96%D0%B2" title="Обробка сигналів – Ukrainian" lang="uk" hreflang="uk" data-title="Обробка сигналів" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B9%D9%85%D9%84%DB%8C%D8%AA_%D8%A7%D8%B4%D8%A7%D8%B1%DB%81" title="عملیت اشارہ – Urdu" lang="ur" hreflang="ur" data-title="عملیت اشارہ" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/X%E1%BB%AD_l%C3%BD_t%C3%ADn_hi%E1%BB%87u" title="Xử lý tín hiệu – Vietnamese" lang="vi" hreflang="vi" data-title="Xử lý tín hiệu" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E4%BF%A1%E5%8F%B7%E5%A4%84%E7%90%86" title="信号处理 – Wu" lang="wuu" hreflang="wuu" data-title="信号处理" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%A8%8A%E8%99%9F%E8%99%95%E7%90%86" title="訊號處理 – Cantonese" lang="yue" hreflang="yue" data-title="訊號處理" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BF%A1%E5%8F%B7%E5%A4%84%E7%90%86" title="信号处理 – Chinese" lang="zh" hreflang="zh" data-title="信号处理" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q208163#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Signal_processing" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Signal_processing" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t"><span>Talk</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Change language variant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">English</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Views"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Signal_processing"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Signal_processing&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Signal_processing&action=history" title="Past revisions of this page [h]" accesskey="h"><span>View history</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Tools" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tools</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Tools</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">hide</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Signal_processing"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Signal_processing&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Signal_processing&action=history"><span>View history</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/Signal_processing" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j"><span>What links here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Signal_processing" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q"><span>Special pages</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Signal_processing&oldid=1258826289" title="Permanent link to this revision of this page"><span>Permanent link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Signal_processing&action=info" title="More information about this page"><span>Page information</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:CiteThisPage&page=Signal_processing&id=1258826289&wpFormIdentifier=titleform" title="Information on how to cite this page"><span>Cite this page</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FSignal_processing"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FSignal_processing"><span>Download QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Print/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Signal_processing&action=show-download-screen" title="Download this page as a PDF file"><span>Download as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Signal_processing&printable=yes" title="Printable version of this page [p]" accesskey="p"><span>Printable version</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In other projects </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Signal_processing" hreflang="en"><span>Wikimedia Commons</span></a></li><li class="wb-otherproject-link wb-otherproject-wikiversity mw-list-item"><a href="https://en.wikiversity.org/wiki/Signal_Processing" hreflang="en"><span>Wikiversity</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q208163" title="Structured data on this page hosted by Wikidata [g]" accesskey="g"><span>Wikidata item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Field of electrical engineering</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Signal theory" redirects here. Not to be confused with <a href="/wiki/Signalling_theory" title="Signalling theory">Signalling theory</a> or <a href="/wiki/Signalling_(economics)" title="Signalling (economics)">Signalling (economics)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><style data-mw-deduplicate="TemplateStyles:r1248332772">.mw-parser-output .multiple-issues-text{width:95%;margin:0.2em 0}.mw-parser-output .multiple-issues-text>.mw-collapsible-content{margin-top:0.3em}.mw-parser-output .compact-ambox .ambox{border:none;border-collapse:collapse;background-color:transparent;margin:0 0 0 1.6em!important;padding:0!important;width:auto;display:block}body.mediawiki .mw-parser-output .compact-ambox .ambox.mbox-small-left{font-size:100%;width:auto;margin:0}.mw-parser-output .compact-ambox .ambox .mbox-text{padding:0!important;margin:0!important}.mw-parser-output .compact-ambox .ambox .mbox-text-span{display:list-item;line-height:1.5em;list-style-type:disc}body.skin-minerva .mw-parser-output .multiple-issues-text>.mw-collapsible-toggle,.mw-parser-output .compact-ambox .ambox .mbox-image,.mw-parser-output .compact-ambox .ambox .mbox-imageright,.mw-parser-output .compact-ambox .ambox .mbox-empty-cell,.mw-parser-output .compact-ambox .hide-when-compact{display:none}</style><table class="box-Multiple_issues plainlinks metadata ambox ambox-content ambox-multiple_issues compact-ambox" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span"><div class="multiple-issues-text mw-collapsible"><b>This article has multiple issues.</b> Please help <b><a href="/wiki/Special:EditPage/Signal_processing" title="Special:EditPage/Signal processing">improve it</a></b> or discuss these issues on the <b><a href="/wiki/Talk:Signal_processing" title="Talk:Signal processing">talk page</a></b>. <small><i>(<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove these messages</a>)</i></small> <div class="mw-collapsible-content"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-More_footnotes_needed plainlinks metadata ambox ambox-style ambox-More_footnotes_needed" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/40px-Text_document_with_red_question_mark.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/60px-Text_document_with_red_question_mark.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Text_document_with_red_question_mark.svg/80px-Text_document_with_red_question_mark.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article includes a list of <a href="/wiki/Wikipedia:Citing_sources#General_references" title="Wikipedia:Citing sources">general references</a>, but <b>it lacks sufficient corresponding <a href="/wiki/Wikipedia:Citing_sources#Inline_citations" title="Wikipedia:Citing sources">inline citations</a></b>.<span class="hide-when-compact"> Please help to <a href="/wiki/Wikipedia:WikiProject_Reliability" title="Wikipedia:WikiProject Reliability">improve</a> this article by <a href="/wiki/Wikipedia:When_to_cite" title="Wikipedia:When to cite">introducing</a> more precise citations.</span> <span class="date-container"><i>(<span class="date">January 2017</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Prose plainlinks metadata ambox ambox-style ambox-Prose" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/40px-Edit-clear.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/60px-Edit-clear.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/f/f2/Edit-clear.svg/80px-Edit-clear.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>is in <a href="/wiki/MOS:LIST" class="mw-redirect" title="MOS:LIST">list</a> format but may read better as <a href="/wiki/MOS:PROSE" class="mw-redirect" title="MOS:PROSE">prose</a></b>.<span class="hide-when-compact"> You can help by <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Signal_processing&action=edit">converting this article</a>, if appropriate. <a href="/wiki/Help:Editing" title="Help:Editing">Editing help</a> is available.</span> <span class="date-container"><i>(<span class="date">June 2017</span>)</i></span></div></td></tr></tbody></table> </div> </div><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Signal_processing_system.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Signal_processing_system.png/400px-Signal_processing_system.png" decoding="async" width="400" height="129" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Signal_processing_system.png/600px-Signal_processing_system.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/Signal_processing_system.png/800px-Signal_processing_system.png 2x" data-file-width="1204" data-file-height="387" /></a><figcaption>Signal transmission using electronic signal processing. <a href="/wiki/Transducer" title="Transducer">Transducers</a> convert signals from other physical <a href="/wiki/Waveform" title="Waveform">waveforms</a> to electric <a href="/wiki/Electric_current" title="Electric current">current</a> or <a href="/wiki/Voltage" title="Voltage">voltage</a> waveforms, which then are processed, transmitted as <a href="/wiki/Electromagnetic_wave" class="mw-redirect" title="Electromagnetic wave">electromagnetic waves</a>, received and converted by another transducer to final form.</figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:408px;max-width:408px"><div class="trow"><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Cosine_Series_Plus_Noise.png/200px-Cosine_Series_Plus_Noise.png" decoding="async" width="200" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Cosine_Series_Plus_Noise.png/300px-Cosine_Series_Plus_Noise.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/11/Cosine_Series_Plus_Noise.png/400px-Cosine_Series_Plus_Noise.png 2x" data-file-width="1200" data-file-height="900" /></span></span></div></div><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Cosine_Series_Plus_Noise_TFM.png/200px-Cosine_Series_Plus_Noise_TFM.png" decoding="async" width="200" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Cosine_Series_Plus_Noise_TFM.png/300px-Cosine_Series_Plus_Noise_TFM.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Cosine_Series_Plus_Noise_TFM.png/400px-Cosine_Series_Plus_Noise_TFM.png 2x" data-file-width="1200" data-file-height="900" /></span></span></div></div></div><div class="trow" style="display:flex"><div class="thumbcaption">The signal on the left looks like noise, but the signal processing technique known as <a href="/wiki/Spectral_density_estimation" title="Spectral density estimation">spectral density estimation</a> (right) shows that it contains five well-defined frequency components.</div></div></div></div> <p><b>Signal processing</b> is an <a href="/wiki/Electrical_engineering" title="Electrical engineering">electrical engineering</a> subfield that focuses on analyzing, modifying and synthesizing <i><a href="/wiki/Signal" title="Signal">signals</a></i>, such as <a href="/wiki/Audio_signal_processing" title="Audio signal processing">sound</a>, <a href="/wiki/Image_processing" class="mw-redirect" title="Image processing">images</a>, <a href="/wiki/Scalar_potential" title="Scalar potential">potential fields</a>, <a href="/wiki/Seismic_tomography" title="Seismic tomography">seismic signals</a>, <a href="/wiki/Altimeter" title="Altimeter">altimetry processing</a>, and <a href="/wiki/Scientific_measurements" class="mw-redirect" title="Scientific measurements">scientific measurements</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Signal processing techniques are used to optimize transmissions, <a href="/wiki/Data_storage" title="Data storage">digital storage</a> efficiency, correcting distorted signals, improve <a href="/wiki/Subjective_video_quality" title="Subjective video quality">subjective video quality</a>, and to detect or pinpoint components of interest in a measured signal.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal_processing&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>According to <a href="/wiki/Alan_V._Oppenheim" title="Alan V. Oppenheim">Alan V. Oppenheim</a> and <a href="/wiki/Ronald_W._Schafer" title="Ronald W. Schafer">Ronald W. Schafer</a>, the principles of signal processing can be found in the classical <a href="/wiki/Numerical_analysis" title="Numerical analysis">numerical analysis</a> techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital <a href="/wiki/Control_system" title="Control system">control systems</a> of the 1940s and 1950s.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>In 1948, <a href="/wiki/Claude_Shannon" title="Claude Shannon">Claude Shannon</a> wrote the influential paper "<a href="/wiki/A_Mathematical_Theory_of_Communication" title="A Mathematical Theory of Communication">A Mathematical Theory of Communication</a>" which was published in the <i><a href="/wiki/Bell_System_Technical_Journal" class="mw-redirect" title="Bell System Technical Journal">Bell System Technical Journal</a></i>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The paper laid the groundwork for later development of information communication systems and the processing of signals for transmission.<sup id="cite_ref-fifty_5-0" class="reference"><a href="#cite_note-fifty-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>Signal processing matured and flourished in the 1960s and 1970s, and <a href="/wiki/Digital_signal_processing" title="Digital signal processing">digital signal processing</a> became widely used with specialized <a href="/wiki/Digital_signal_processor" title="Digital signal processor">digital signal processor</a> chips in the 1980s.<sup id="cite_ref-fifty_5-1" class="reference"><a href="#cite_note-fifty-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Definition_of_a_signal">Definition of a signal</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal_processing&action=edit&section=2" title="Edit section: Definition of a signal"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A signal is a <a href="/wiki/Function_(mathematics)" title="Function (mathematics)">function</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d54c275db3a1e620737b58e143b0818107fa5f5c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.979ex; height:2.843ex;" alt="{\displaystyle x(t)}"></span>, where this function is either<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <ul><li>deterministic (then one speaks of a deterministic signal) or</li> <li>a path <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x_{t})_{t\in T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>∈</mo> <mi>T</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x_{t})_{t\in T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f1396498f56d9580f5b1625df064d63e84ab5b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.044ex; height:2.843ex;" alt="{\displaystyle (x_{t})_{t\in T}}"></span>, a realization of a <a href="/wiki/Stochastic_process" title="Stochastic process">stochastic process</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (X_{t})_{t\in T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mo>∈</mo> <mi>T</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (X_{t})_{t\in T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f05f8b9d621c0c80afa86a7198ba021247d3a40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.639ex; height:2.843ex;" alt="{\displaystyle (X_{t})_{t\in T}}"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Categories">Categories</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal_processing&action=edit&section=3" title="Edit section: Categories"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Analog">Analog</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal_processing&action=edit&section=4" title="Edit section: Analog"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Analog_signal_processing" title="Analog signal processing">Analog signal processing</a></div> <p>Analog signal processing is for signals that have not been digitized, as in most 20th-century <a href="/wiki/Radio" title="Radio">radio</a>, telephone, and television systems. This involves linear electronic circuits as well as nonlinear ones. The former are, for instance, <a href="/wiki/Passive_filter" class="mw-redirect" title="Passive filter">passive filters</a>, <a href="/wiki/Active_filter" title="Active filter">active filters</a>, <a href="/wiki/Electronic_mixer" title="Electronic mixer">additive mixers</a>, <a href="/wiki/Integrator" title="Integrator">integrators</a>, and <a href="/wiki/Analog_delay_line" title="Analog delay line">delay lines</a>. Nonlinear circuits include <a href="/wiki/Compandor" class="mw-redirect" title="Compandor">compandors</a>, multipliers (<a href="/wiki/Frequency_mixer" title="Frequency mixer">frequency mixers</a>, <a href="/wiki/Voltage-controlled_amplifier" class="mw-redirect" title="Voltage-controlled amplifier">voltage-controlled amplifiers</a>), <a href="/wiki/Voltage-controlled_filter" title="Voltage-controlled filter">voltage-controlled filters</a>, <a href="/wiki/Voltage-controlled_oscillator" title="Voltage-controlled oscillator">voltage-controlled oscillators</a>, and <a href="/wiki/Phase-locked_loop" title="Phase-locked loop">phase-locked loops</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Continuous_time">Continuous time</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal_processing&action=edit&section=5" title="Edit section: Continuous time"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Continuous_signal" class="mw-redirect" title="Continuous signal">Continuous-time signal</a> processing is for signals that vary with the change of continuous domain (without considering some individual interrupted points). </p><p>The methods of signal processing include <a href="/wiki/Time_domain" title="Time domain">time domain</a>, <a href="/wiki/Frequency_domain" title="Frequency domain">frequency domain</a>, and <a href="/wiki/Complex_frequency" class="mw-redirect" title="Complex frequency">complex frequency domain</a>. This technology mainly discusses the modeling of a linear time-invariant continuous system, integral of the system's zero-state response, setting up system function and the continuous time filtering of deterministic signals </p> <div class="mw-heading mw-heading3"><h3 id="Discrete_time">Discrete time</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal_processing&action=edit&section=6" title="Edit section: Discrete time"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Discrete-time_signal" class="mw-redirect" title="Discrete-time signal">Discrete-time signal</a> processing is for sampled signals, defined only at discrete points in time, and as such are quantized in time, but not in magnitude. </p><p><i>Analog discrete-time signal processing</i> is a technology based on electronic devices such as <a href="/wiki/Sample_and_hold" title="Sample and hold">sample and hold</a> circuits, analog time-division <a href="/wiki/Multiplexer" title="Multiplexer">multiplexers</a>, <a href="/wiki/Analog_delay_line" title="Analog delay line">analog delay lines</a> and <a href="/wiki/Analog_feedback_shift_register" title="Analog feedback shift register">analog feedback shift registers</a>. This technology was a predecessor of digital signal processing (see below), and is still used in advanced processing of gigahertz signals.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>The concept of discrete-time signal processing also refers to a theoretical discipline that establishes a mathematical basis for digital signal processing, without taking <a href="/wiki/Quantization_error" class="mw-redirect" title="Quantization error">quantization error</a> into consideration. </p> <div class="mw-heading mw-heading3"><h3 id="Digital">Digital</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal_processing&action=edit&section=7" title="Edit section: Digital"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Digital_signal_processing" title="Digital signal processing">Digital signal processing</a></div> <p>Digital signal processing is the processing of digitized discrete-time sampled signals. Processing is done by general-purpose <a href="/wiki/Computer" title="Computer">computers</a> or by digital circuits such as <a href="/wiki/ASIC" class="mw-redirect" title="ASIC">ASICs</a>, <a href="/wiki/Field-programmable_gate_array" title="Field-programmable gate array">field-programmable gate arrays</a> or specialized <a href="/wiki/Digital_signal_processor" title="Digital signal processor">digital signal processors</a>. Typical arithmetical operations include <a href="/wiki/Fixed-point_arithmetic" title="Fixed-point arithmetic">fixed-point</a> and <a href="/wiki/Floating-point" class="mw-redirect" title="Floating-point">floating-point</a>, real-valued and complex-valued, multiplication and addition. Other typical operations supported by the hardware are <a href="/wiki/Circular_buffer" title="Circular buffer">circular buffers</a> and <a href="/wiki/Lookup_table" title="Lookup table">lookup tables</a>. Examples of algorithms are the <a href="/wiki/Fast_Fourier_transform" title="Fast Fourier transform">fast Fourier transform</a> (FFT), <a href="/wiki/Finite_impulse_response" title="Finite impulse response">finite impulse response</a> (FIR) filter, <a href="/wiki/Infinite_impulse_response" title="Infinite impulse response">Infinite impulse response</a> (IIR) filter, and <a href="/wiki/Adaptive_filter" title="Adaptive filter">adaptive filters</a> such as the <a href="/wiki/Wiener_filter" title="Wiener filter">Wiener</a> and <a href="/wiki/Kalman_filter" title="Kalman filter">Kalman filters</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Nonlinear">Nonlinear</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal_processing&action=edit&section=8" title="Edit section: Nonlinear"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Nonlinear_system" title="Nonlinear system">Nonlinear signal processing</a> involves the analysis and processing of signals produced from nonlinear systems and can be in the time, <a href="/wiki/Frequency" title="Frequency">frequency</a>, or spatiotemporal domains.<sup id="cite_ref-Billings_8-0" class="reference"><a href="#cite_note-Billings-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-VSA_9-0" class="reference"><a href="#cite_note-VSA-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Nonlinear_systems" class="mw-redirect" title="Nonlinear systems">Nonlinear systems</a> can produce highly complex behaviors including <a href="/wiki/Bifurcation_theory" title="Bifurcation theory">bifurcations</a>, <a href="/wiki/Chaos_theory" title="Chaos theory">chaos</a>, <a href="/wiki/Harmonics" class="mw-redirect" title="Harmonics">harmonics</a>, and <a href="/wiki/Subharmonics" class="mw-redirect" title="Subharmonics">subharmonics</a> which cannot be produced or analyzed using linear methods. </p><p>Polynomial signal processing is a type of non-linear signal processing, where <a href="/wiki/Polynomial" title="Polynomial">polynomial</a> systems may be interpreted as conceptually straightforward extensions of linear systems to the non-linear case.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Statistical">Statistical</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal_processing&action=edit&section=9" title="Edit section: Statistical"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Statistical signal processing</b> is an approach which treats signals as <a href="/wiki/Stochastic_process" title="Stochastic process">stochastic processes</a>, utilizing their <a href="/wiki/Statistical" class="mw-redirect" title="Statistical">statistical</a> properties to perform signal processing tasks.<sup id="cite_ref-Scharf_11-0" class="reference"><a href="#cite_note-Scharf-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Statistical techniques are widely used in signal processing applications. For example, one can model the <a href="/wiki/Probability_distribution" title="Probability distribution">probability distribution</a> of noise incurred when photographing an image, and construct techniques based on this model to <a href="/wiki/Noise_reduction" title="Noise reduction">reduce the noise</a> in the resulting image. </p> <div class="mw-heading mw-heading2"><h2 id="Application_fields">Application fields</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal_processing&action=edit&section=10" title="Edit section: Application fields"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Seismic_Data_Processing.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Seismic_Data_Processing.jpg/220px-Seismic_Data_Processing.jpg" decoding="async" width="220" height="148" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Seismic_Data_Processing.jpg/330px-Seismic_Data_Processing.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Seismic_Data_Processing.jpg/440px-Seismic_Data_Processing.jpg 2x" data-file-width="662" data-file-height="446" /></a><figcaption>Seismic signal processing</figcaption></figure> <ul><li><a href="/wiki/Audio_signal_processing" title="Audio signal processing">Audio signal processing</a> –  for electrical signals representing sound, such as <a href="/wiki/Speech_signal_processing" class="mw-redirect" title="Speech signal processing">speech</a> or music<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Image_processing" class="mw-redirect" title="Image processing">Image processing</a> –  in digital cameras, computers and various imaging systems</li> <li><a href="/wiki/Video_processing" title="Video processing">Video processing</a> –  for interpreting moving pictures</li> <li><a href="/wiki/Wireless_communication" class="mw-redirect" title="Wireless communication">Wireless communication</a> –  waveform generations, demodulation, filtering, equalization</li> <li><a href="/wiki/Control_systems" class="mw-redirect" title="Control systems">Control systems</a></li> <li><a href="/wiki/Array_processing" title="Array processing">Array processing</a> –  for processing signals from arrays of sensors</li> <li><a href="/wiki/Process_control" class="mw-redirect" title="Process control">Process control</a> –  a variety of signals are used, including the industry standard 4-20 mA <a href="/wiki/Current_loop" title="Current loop">current loop</a></li> <li><a href="/wiki/Seismology" title="Seismology">Seismology</a></li> <li><a href="/wiki/Feature_extraction" class="mw-redirect" title="Feature extraction">Feature extraction</a>, such as <a href="/wiki/Image_understanding" class="mw-redirect" title="Image understanding">image understanding</a> and <a href="/wiki/Speech_recognition" title="Speech recognition">speech recognition</a>.</li> <li>Quality improvement, such as <a href="/wiki/Noise_reduction" title="Noise reduction">noise reduction</a>, <a href="/wiki/Image_enhancement" class="mw-redirect" title="Image enhancement">image enhancement</a>, and <a href="/wiki/Echo_cancellation" class="mw-redirect" title="Echo cancellation">echo cancellation</a>.</li> <li>Source coding including <a href="/wiki/Audio_compression_(data)" class="mw-redirect" title="Audio compression (data)">audio compression</a>, <a href="/wiki/Image_compression" title="Image compression">image compression</a>, and <a href="/wiki/Video_compression" class="mw-redirect" title="Video compression">video compression</a>.</li> <li><a href="/wiki/Genomic" class="mw-redirect" title="Genomic">Genomic</a> signal processing<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup></li> <li>In <a href="/wiki/Geophysics" title="Geophysics">geophysics</a>, signal processing is used to amplify the signal vs the noise within <a href="/wiki/Time-series" class="mw-redirect" title="Time-series">time-series</a> measurements of geophysical data. Processing is conducted within either the <a href="/wiki/Time_domain" title="Time domain">time domain</a> or <a href="/wiki/Frequency_domain" title="Frequency domain">frequency domain</a>, or both.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup></li></ul> <p>In communication systems, signal processing may occur at: </p> <ul><li>OSI layer 1 in the seven-layer <a href="/wiki/OSI_model" title="OSI model">OSI model</a>, the <a href="/wiki/Physical_layer" title="Physical layer">physical layer</a> (<a href="/wiki/Modulation" title="Modulation">modulation</a>, <a href="/wiki/Equalization_(communications)" title="Equalization (communications)">equalization</a>, <a href="/wiki/Multiplexing" title="Multiplexing">multiplexing</a>, etc.);</li> <li>OSI layer 2, the <a href="/wiki/Data_link_layer" title="Data link layer">data link layer</a> (<a href="/wiki/Forward_error_correction" class="mw-redirect" title="Forward error correction">forward error correction</a>);</li> <li>OSI layer 6, the <a href="/wiki/Presentation_layer" title="Presentation layer">presentation layer</a> (source coding, including <a href="/wiki/Analog-to-digital_conversion" class="mw-redirect" title="Analog-to-digital conversion">analog-to-digital conversion</a> and <a href="/wiki/Data_compression" title="Data compression">data compression</a>).</li></ul> <div class="mw-heading mw-heading2"><h2 id="Typical_devices">Typical devices</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal_processing&action=edit&section=11" title="Edit section: Typical devices"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Filter_(signal_processing)" title="Filter (signal processing)">Filters</a> –  for example analog (passive or active) or digital (<a href="/wiki/FIR_filter" class="mw-redirect" title="FIR filter">FIR</a>, <a href="/wiki/IIR_filter" class="mw-redirect" title="IIR filter">IIR</a>, frequency domain or <a href="/wiki/Stochastic_filter" class="mw-redirect" title="Stochastic filter">stochastic filters</a>, etc.)</li> <li><a href="/wiki/Sampling_(signal_processing)" title="Sampling (signal processing)">Samplers</a> and <a href="/wiki/Analog-to-digital_converter" title="Analog-to-digital converter">analog-to-digital converters</a> for <a href="/wiki/Data_acquisition" title="Data acquisition">signal acquisition</a> and reconstruction, which involves measuring a physical signal, storing or transferring it as digital signal, and possibly later rebuilding the original signal or an approximation thereof.</li> <li><a href="/wiki/Data_compression" title="Data compression">Signal compressors</a></li> <li><a href="/wiki/Digital_signal_processor" title="Digital signal processor">Digital signal processors</a> (DSPs)</li></ul> <div class="mw-heading mw-heading2"><h2 id="Mathematical_methods_applied">Mathematical methods applied</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal_processing&action=edit&section=12" title="Edit section: Mathematical methods applied"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Differential_equations" class="mw-redirect" title="Differential equations">Differential equations</a><sup id="cite_ref-Gaydecki2004_16-0" class="reference"><a href="#cite_note-Gaydecki2004-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Recurrence_relation" title="Recurrence relation">Recurrence relations</a><sup id="cite_ref-Engelberg2008_17-0" class="reference"><a href="#cite_note-Engelberg2008-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Transform_theory" title="Transform theory">Transform theory</a></li> <li><a href="/wiki/Time-frequency_analysis" class="mw-redirect" title="Time-frequency analysis">Time-frequency analysis</a> –  for processing non-stationary signals<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Spectral_estimation" class="mw-redirect" title="Spectral estimation">Spectral estimation</a> –  for determining the spectral content (i.e., the distribution of power over frequency) of a <a href="/wiki/Time_series" title="Time series">time series</a><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Statistical_signal_processing" class="mw-redirect" title="Statistical signal processing">Statistical signal processing</a> –  analyzing and extracting information from signals and noise based on their stochastic properties</li> <li><a href="/wiki/Linear_time-invariant_system" title="Linear time-invariant system">Linear time-invariant system</a> theory, and <a href="/wiki/Transform_theory" title="Transform theory">transform theory</a></li> <li><a href="/wiki/Polynomial_signal_processing" class="mw-redirect" title="Polynomial signal processing">Polynomial signal processing</a> –  analysis of systems which relate input and output using polynomials</li> <li><a href="/wiki/System_identification" title="System identification">System identification</a><sup id="cite_ref-Billings_8-1" class="reference"><a href="#cite_note-Billings-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> and classification</li> <li><a href="/wiki/Calculus" title="Calculus">Calculus</a></li> <li><a href="/wiki/Code" title="Code">Code</a></li> <li><a href="/wiki/Complex_analysis" title="Complex analysis">Complex analysis</a><sup id="cite_ref-SchreierScharf2010_20-0" class="reference"><a href="#cite_note-SchreierScharf2010-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Vector_spaces" class="mw-redirect" title="Vector spaces">Vector spaces</a> and <a href="/wiki/Linear_algebra" title="Linear algebra">Linear algebra</a><sup id="cite_ref-Little2019_21-0" class="reference"><a href="#cite_note-Little2019-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Functional_analysis" title="Functional analysis">Functional analysis</a><sup id="cite_ref-DamelinJr2012_22-0" class="reference"><a href="#cite_note-DamelinJr2012-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Probability" title="Probability">Probability</a> and <a href="/wiki/Stochastic_processes" class="mw-redirect" title="Stochastic processes">stochastic processes</a><sup id="cite_ref-Scharf_11-1" class="reference"><a href="#cite_note-Scharf-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Detection_theory" title="Detection theory">Detection theory</a></li> <li><a href="/wiki/Estimation_theory" title="Estimation theory">Estimation theory</a></li> <li><a href="/wiki/Optimization" class="mw-redirect" title="Optimization">Optimization</a><sup id="cite_ref-PalomarEldar2010_23-0" class="reference"><a href="#cite_note-PalomarEldar2010-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Numerical_methods" class="mw-redirect" title="Numerical methods">Numerical methods</a></li> <li><a href="/wiki/Time_series" title="Time series">Time series</a></li> <li><a href="/wiki/Data_mining" title="Data mining">Data mining</a> –  for statistical analysis of relations between large quantities of variables (in this context representing many physical signals), to extract previously unknown interesting patterns</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal_processing&action=edit&section=13" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Algebraic_signal_processing" title="Algebraic signal processing">Algebraic signal processing</a></li> <li><a href="/wiki/Audio_filter" title="Audio filter">Audio filter</a></li> <li><a href="/wiki/Bounded_variation" title="Bounded variation">Bounded variation</a></li> <li><a href="/wiki/Digital_image_processing" title="Digital image processing">Digital image processing</a></li> <li><a href="/wiki/Dynamic_range_compression" title="Dynamic range compression">Dynamic range compression</a>, <a href="/wiki/Companding" title="Companding">companding</a>, <a href="/wiki/Limiting" class="mw-redirect" title="Limiting">limiting</a>, and <a href="/wiki/Noise_gating" class="mw-redirect" title="Noise gating">noise gating</a></li> <li><a href="/wiki/Fourier_transform" title="Fourier transform">Fourier transform</a></li> <li><a href="/wiki/Information_theory" title="Information theory">Information theory</a></li> <li><a href="/wiki/Least-squares_spectral_analysis" title="Least-squares spectral analysis">Least-squares spectral analysis</a></li> <li><a href="/wiki/Non-local_means" title="Non-local means">Non-local means</a></li> <li><a href="/wiki/Reverberation" title="Reverberation">Reverberation</a></li> <li><a href="/wiki/Sensitivity_(electronics)" title="Sensitivity (electronics)">Sensitivity (electronics)</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal_processing&action=edit&section=14" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFSenguptaSahidullah,_MdSaha,_Goutam2016" class="citation journal cs1">Sengupta, Nandini; Sahidullah, Md; Saha, Goutam (August 2016). "Lung sound classification using cepstral-based statistical features". <i>Computers in Biology and Medicine</i>. <b>75</b> (1): 118–129. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.compbiomed.2016.05.013">10.1016/j.compbiomed.2016.05.013</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/27286184">27286184</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Computers+in+Biology+and+Medicine&rft.atitle=Lung+sound+classification+using+cepstral-based+statistical+features&rft.volume=75&rft.issue=1&rft.pages=118-129&rft.date=2016-08&rft_id=info%3Adoi%2F10.1016%2Fj.compbiomed.2016.05.013&rft_id=info%3Apmid%2F27286184&rft.aulast=Sengupta&rft.aufirst=Nandini&rft.au=Sahidullah%2C+Md&rft.au=Saha%2C+Goutam&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAlan_V._Oppenheim_and_Ronald_W._Schafer1989" class="citation book cs1">Alan V. Oppenheim and Ronald W. Schafer (1989). <i>Discrete-Time Signal Processing</i>. Prentice Hall. p. 1. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-13-216771-9" title="Special:BookSources/0-13-216771-9"><bdi>0-13-216771-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Discrete-Time+Signal+Processing&rft.pages=1&rft.pub=Prentice+Hall&rft.date=1989&rft.isbn=0-13-216771-9&rft.au=Alan+V.+Oppenheim+and+Ronald+W.+Schafer&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOppenheim,_Alan_V.Schafer,_Ronald_W.1975" class="citation book cs1">Oppenheim, Alan V.; Schafer, Ronald W. (1975). <i>Digital Signal Processing</i>. <a href="/wiki/Prentice_Hall" title="Prentice Hall">Prentice Hall</a>. p. 5. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-13-214635-5" title="Special:BookSources/0-13-214635-5"><bdi>0-13-214635-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Digital+Signal+Processing&rft.pages=5&rft.pub=Prentice+Hall&rft.date=1975&rft.isbn=0-13-214635-5&rft.au=Oppenheim%2C+Alan+V.&rft.au=Schafer%2C+Ronald+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.computerhistory.org/revolution/digital-logic/12/269/1331">"A Mathematical Theory of Communication – CHM Revolution"</a>. <i>Computer History</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2019-05-13</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Computer+History&rft.atitle=A+Mathematical+Theory+of+Communication+%E2%80%93+CHM+Revolution&rft_id=https%3A%2F%2Fwww.computerhistory.org%2Frevolution%2Fdigital-logic%2F12%2F269%2F1331&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-fifty-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-fifty_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-fifty_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://signalprocessingsociety.org/uploads/history/history.pdf"><i>Fifty Years of Signal Processing: The IEEE Signal Processing Society and its Technologies, 1948–1998</i></a> <span class="cs1-format">(PDF)</span>. The IEEE Signal Processing Society. 1998.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fifty+Years+of+Signal+Processing%3A+The+IEEE+Signal+Processing+Society+and+its+Technologies%2C+1948%E2%80%931998&rft.pub=The+IEEE+Signal+Processing+Society&rft.date=1998&rft_id=https%3A%2F%2Fsignalprocessingsociety.org%2Fuploads%2Fhistory%2Fhistory.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Berber, S. (2021). Discrete Communication Systems. United Kingdom: Oxford University Press., page 9, <a rel="nofollow" class="external free" href="https://books.google.com/books?id=CCs0EAAAQBAJ&pg=PA9">https://books.google.com/books?id=CCs0EAAAQBAJ&pg=PA9</a></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://microwavelab.nd.edu/research/analog-signal-processing/">"Microwave & Millimeter-wave Circuits and Systems"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-10-20</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Microwave+%26+Millimeter-wave+Circuits+and+Systems&rft_id=https%3A%2F%2Fmicrowavelab.nd.edu%2Fresearch%2Fanalog-signal-processing%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-Billings-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-Billings_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Billings_8-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBillings2013" class="citation book cs1">Billings, S. A. (2013). <i>Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains</i>. Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-119-94359-4" title="Special:BookSources/978-1-119-94359-4"><bdi>978-1-119-94359-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Nonlinear+System+Identification%3A+NARMAX+Methods+in+the+Time%2C+Frequency%2C+and+Spatio-Temporal+Domains&rft.pub=Wiley&rft.date=2013&rft.isbn=978-1-119-94359-4&rft.aulast=Billings&rft.aufirst=S.+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-VSA-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-VSA_9-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSlawinska,_J.Ourmazd,_A.Giannakis,_D.2018" class="citation book cs1">Slawinska, J.; Ourmazd, A.; Giannakis, D. (2018). "A New Approach to Signal Processing of Spatiotemporal Data". <i>2018 IEEE Statistical Signal Processing Workshop (SSP)</i>. IEEE Xplore. pp. 338–342. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FSSP.2018.8450704">10.1109/SSP.2018.8450704</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-5386-1571-3" title="Special:BookSources/978-1-5386-1571-3"><bdi>978-1-5386-1571-3</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:52153144">52153144</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=A+New+Approach+to+Signal+Processing+of+Spatiotemporal+Data&rft.btitle=2018+IEEE+Statistical+Signal+Processing+Workshop+%28SSP%29&rft.pages=338-342&rft.pub=IEEE+Xplore&rft.date=2018&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A52153144%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FSSP.2018.8450704&rft.isbn=978-1-5386-1571-3&rft.au=Slawinska%2C+J.&rft.au=Ourmazd%2C+A.&rft.au=Giannakis%2C+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFV._John_MathewsGiovanni_L._Sicuranza2000" class="citation book cs1">V. John Mathews; Giovanni L. Sicuranza (May 2000). <i>Polynomial Signal Processing</i>. Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-03414-8" title="Special:BookSources/978-0-471-03414-8"><bdi>978-0-471-03414-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Polynomial+Signal+Processing&rft.pub=Wiley&rft.date=2000-05&rft.isbn=978-0-471-03414-8&rft.au=V.+John+Mathews&rft.au=Giovanni+L.+Sicuranza&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-Scharf-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-Scharf_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Scharf_11-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFScharf1991" class="citation book cs1">Scharf, Louis L. (1991). <i>Statistical signal processing: detection, estimation, and time series analysis</i>. <a href="/wiki/Boston" title="Boston">Boston</a>: <a href="/wiki/Addison%E2%80%93Wesley" class="mw-redirect" title="Addison–Wesley">Addison–Wesley</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-201-19038-9" title="Special:BookSources/0-201-19038-9"><bdi>0-201-19038-9</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/61160161">61160161</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Statistical+signal+processing%3A+detection%2C+estimation%2C+and+time+series+analysis&rft.place=Boston&rft.pub=Addison%E2%80%93Wesley&rft.date=1991&rft_id=info%3Aoclcnum%2F61160161&rft.isbn=0-201-19038-9&rft.aulast=Scharf&rft.aufirst=Louis+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSarangiSahidullah,_MdSaha,_Goutam2020" class="citation journal cs1">Sarangi, Susanta; Sahidullah, Md; Saha, Goutam (September 2020). "Optimization of data-driven filterbank for automatic speaker verification". <i>Digital Signal Processing</i>. <b>104</b>: 102795. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/2007.10729">2007.10729</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2020DSP...10402795S">2020DSP...10402795S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.dsp.2020.102795">10.1016/j.dsp.2020.102795</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:220665533">220665533</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Digital+Signal+Processing&rft.atitle=Optimization+of+data-driven+filterbank+for+automatic+speaker+verification&rft.volume=104&rft.pages=102795&rft.date=2020-09&rft_id=info%3Aarxiv%2F2007.10729&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A220665533%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1016%2Fj.dsp.2020.102795&rft_id=info%3Abibcode%2F2020DSP...10402795S&rft.aulast=Sarangi&rft.aufirst=Susanta&rft.au=Sahidullah%2C+Md&rft.au=Saha%2C+Goutam&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAnastassiou2001" class="citation journal cs1">Anastassiou, D. (2001). "Genomic signal processing". <i>IEEE Signal Processing Magazine</i>. <b>18</b> (4). IEEE: 8–20. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001ISPM...18....8A">2001ISPM...18....8A</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F79.939833">10.1109/79.939833</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Signal+Processing+Magazine&rft.atitle=Genomic+signal+processing&rft.volume=18&rft.issue=4&rft.pages=8-20&rft.date=2001&rft_id=info%3Adoi%2F10.1109%2F79.939833&rft_id=info%3Abibcode%2F2001ISPM...18....8A&rft.aulast=Anastassiou&rft.aufirst=D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTelfordGeldartSheriff1990" class="citation book cs1">Telford, William Murray; Geldart, L. P.; Sheriff, Robert E. (1990). <i>Applied geophysics</i>. <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-33938-4" title="Special:BookSources/978-0-521-33938-4"><bdi>978-0-521-33938-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Applied+geophysics&rft.pub=Cambridge+University+Press&rft.date=1990&rft.isbn=978-0-521-33938-4&rft.aulast=Telford&rft.aufirst=William+Murray&rft.au=Geldart%2C+L.+P.&rft.au=Sheriff%2C+Robert+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFReynolds2011" class="citation book cs1">Reynolds, John M. (2011). <i>An Introduction to Applied and Environmental Geophysics</i>. <a href="/wiki/Wiley-Blackwell" title="Wiley-Blackwell">Wiley-Blackwell</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-48535-3" title="Special:BookSources/978-0-471-48535-3"><bdi>978-0-471-48535-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Introduction+to+Applied+and+Environmental+Geophysics&rft.pub=Wiley-Blackwell&rft.date=2011&rft.isbn=978-0-471-48535-3&rft.aulast=Reynolds&rft.aufirst=John+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-Gaydecki2004-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-Gaydecki2004_16-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPatrick_Gaydecki2004" class="citation book cs1">Patrick Gaydecki (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=6Qo7NvX3vz4C&q=%22differential+equation%22+OR+%22differential+equations%22&pg=PA40"><i>Foundations of Digital Signal Processing: Theory, Algorithms and Hardware Design</i></a>. IET. pp. 40–. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-85296-431-6" title="Special:BookSources/978-0-85296-431-6"><bdi>978-0-85296-431-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Foundations+of+Digital+Signal+Processing%3A+Theory%2C+Algorithms+and+Hardware+Design&rft.pages=40-&rft.pub=IET&rft.date=2004&rft.isbn=978-0-85296-431-6&rft.au=Patrick+Gaydecki&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D6Qo7NvX3vz4C%26q%3D%2522differential%2Bequation%2522%2BOR%2B%2522differential%2Bequations%2522%26pg%3DPA40&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-Engelberg2008-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-Engelberg2008_17-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShlomo_Engelberg2008" class="citation book cs1">Shlomo Engelberg (8 January 2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=z3CpcCHbtgIC"><i>Digital Signal Processing: An Experimental Approach</i></a>. Springer Science & Business Media. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-84800-119-0" title="Special:BookSources/978-1-84800-119-0"><bdi>978-1-84800-119-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Digital+Signal+Processing%3A+An+Experimental+Approach&rft.pub=Springer+Science+%26+Business+Media&rft.date=2008-01-08&rft.isbn=978-1-84800-119-0&rft.au=Shlomo+Engelberg&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dz3CpcCHbtgIC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBoashash,_Boualem2003" class="citation book cs1">Boashash, Boualem, ed. (2003). <i>Time frequency signal analysis and processing a comprehensive reference</i> (1 ed.). Amsterdam: Elsevier. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-08-044335-4" title="Special:BookSources/0-08-044335-4"><bdi>0-08-044335-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Time+frequency+signal+analysis+and+processing+a+comprehensive+reference&rft.place=Amsterdam&rft.edition=1&rft.pub=Elsevier&rft.date=2003&rft.isbn=0-08-044335-4&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStoicaMoses2005" class="citation book cs1">Stoica, Petre; Moses, Randolph (2005). <a rel="nofollow" class="external text" href="http://user.it.uu.se/%7Eps/SAS-new.pdf"><i>Spectral Analysis of Signals</i></a> <span class="cs1-format">(PDF)</span>. NJ: Prentice Hall.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Spectral+Analysis+of+Signals&rft.place=NJ&rft.pub=Prentice+Hall&rft.date=2005&rft.aulast=Stoica&rft.aufirst=Petre&rft.au=Moses%2C+Randolph&rft_id=http%3A%2F%2Fuser.it.uu.se%2F%257Eps%2FSAS-new.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-SchreierScharf2010-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-SchreierScharf2010_20-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPeter_J._SchreierLouis_L._Scharf2010" class="citation book cs1">Peter J. Schreier; Louis L. Scharf (4 February 2010). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=HBaxLfDsAHoC&q=%22complex+analysis%22"><i>Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals</i></a>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-139-48762-7" title="Special:BookSources/978-1-139-48762-7"><bdi>978-1-139-48762-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Statistical+Signal+Processing+of+Complex-Valued+Data%3A+The+Theory+of+Improper+and+Noncircular+Signals&rft.pub=Cambridge+University+Press&rft.date=2010-02-04&rft.isbn=978-1-139-48762-7&rft.au=Peter+J.+Schreier&rft.au=Louis+L.+Scharf&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DHBaxLfDsAHoC%26q%3D%2522complex%2Banalysis%2522&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-Little2019-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-Little2019_21-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMax_A._Little2019" class="citation book cs1">Max A. Little (13 August 2019). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ejGoDwAAQBAJ&q=%22vector+space%22"><i>Machine Learning for Signal Processing: Data Science, Algorithms, and Computational Statistics</i></a>. OUP Oxford. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-102431-3" title="Special:BookSources/978-0-19-102431-3"><bdi>978-0-19-102431-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Machine+Learning+for+Signal+Processing%3A+Data+Science%2C+Algorithms%2C+and+Computational+Statistics&rft.pub=OUP+Oxford&rft.date=2019-08-13&rft.isbn=978-0-19-102431-3&rft.au=Max+A.+Little&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DejGoDwAAQBAJ%26q%3D%2522vector%2Bspace%2522&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-DamelinJr2012-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-DamelinJr2012_22-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSteven_B._DamelinWillard_Miller,_Jr2012" class="citation book cs1">Steven B. Damelin; Willard Miller, Jr (2012). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=MtPLYXQ9d9MC&q=%22functional+analysis%22"><i>The Mathematics of Signal Processing</i></a>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-107-01322-3" title="Special:BookSources/978-1-107-01322-3"><bdi>978-1-107-01322-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mathematics+of+Signal+Processing&rft.pub=Cambridge+University+Press&rft.date=2012&rft.isbn=978-1-107-01322-3&rft.au=Steven+B.+Damelin&rft.au=Willard+Miller%2C+Jr&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DMtPLYXQ9d9MC%26q%3D%2522functional%2Banalysis%2522&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> <li id="cite_note-PalomarEldar2010-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-PalomarEldar2010_23-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDaniel_P._PalomarYonina_C._Eldar2010" class="citation book cs1">Daniel P. Palomar; Yonina C. Eldar (2010). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=UOpnvPJ151gC"><i>Convex Optimization in Signal Processing and Communications</i></a>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-76222-9" title="Special:BookSources/978-0-521-76222-9"><bdi>978-0-521-76222-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Convex+Optimization+in+Signal+Processing+and+Communications&rft.pub=Cambridge+University+Press&rft.date=2010&rft.isbn=978-0-521-76222-9&rft.au=Daniel+P.+Palomar&rft.au=Yonina+C.+Eldar&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DUOpnvPJ151gC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal_processing&action=edit&section=15" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFP_Stoica2005" class="citation book cs1">P Stoica, R Moses (2005). <a rel="nofollow" class="external text" href="http://user.it.uu.se/%7Eps/SAS-new.pdf"><i>Spectral Analysis of Signals</i></a> <span class="cs1-format">(PDF)</span>. NJ: Prentice Hall.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Spectral+Analysis+of+Signals&rft.place=NJ&rft.pub=Prentice+Hall&rft.date=2005&rft.aulast=P+Stoica&rft.aufirst=R+Moses&rft_id=http%3A%2F%2Fuser.it.uu.se%2F%257Eps%2FSAS-new.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKay1993" class="citation book cs1">Kay, Steven M. (1993). <i>Fundamentals of Statistical Signal Processing</i>. <a href="/wiki/Upper_Saddle_River,_New_Jersey" title="Upper Saddle River, New Jersey">Upper Saddle River, New Jersey</a>: <a href="/wiki/Prentice_Hall" title="Prentice Hall">Prentice Hall</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-13-345711-7" title="Special:BookSources/0-13-345711-7"><bdi>0-13-345711-7</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/26504848">26504848</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Statistical+Signal+Processing&rft.place=Upper+Saddle+River%2C+New+Jersey&rft.pub=Prentice+Hall&rft.date=1993&rft_id=info%3Aoclcnum%2F26504848&rft.isbn=0-13-345711-7&rft.aulast=Kay&rft.aufirst=Steven+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPapoulis1991" class="citation book cs1">Papoulis, Athanasios (1991). <i>Probability, Random Variables, and Stochastic Processes</i> (third ed.). McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-07-100870-5" title="Special:BookSources/0-07-100870-5"><bdi>0-07-100870-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Probability%2C+Random+Variables%2C+and+Stochastic+Processes&rft.edition=third&rft.pub=McGraw-Hill&rft.date=1991&rft.isbn=0-07-100870-5&rft.aulast=Papoulis&rft.aufirst=Athanasios&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal+processing" class="Z3988"></span></li> <li>Kainam Thomas Wong <a rel="nofollow" class="external autonumber" href="http://www.eie.polyu.edu.hk/~enktwong/">[1]</a>: Statistical Signal Processing lecture notes at the University of Waterloo, Canada.</li> <li><a href="/wiki/Ali_H._Sayed" title="Ali H. Sayed">Ali H. Sayed</a>, Adaptive Filters, Wiley, NJ, 2008, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-470-25388-5" title="Special:BookSources/978-0-470-25388-5">978-0-470-25388-5</a>.</li> <li><a href="/wiki/Thomas_Kailath" title="Thomas Kailath">Thomas Kailath</a>, <a href="/wiki/Ali_H._Sayed" title="Ali H. Sayed">Ali H. Sayed</a>, and <a href="/wiki/Babak_Hassibi" title="Babak Hassibi">Babak Hassibi</a>, Linear Estimation, Prentice-Hall, NJ, 2000, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-022464-4" title="Special:BookSources/978-0-13-022464-4">978-0-13-022464-4</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal_processing&action=edit&section=16" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://www.sp4comm.org/">Signal Processing for Communications</a> – free online textbook by Paolo Prandoni and Martin Vetterli (2008)</li> <li><a rel="nofollow" class="external text" href="http://www.dspguide.com">Scientists and Engineers Guide to Digital Signal Processing</a> – free online textbook by Stephen Smith</li> <li><a rel="nofollow" class="external text" href="https://www.dsprelated.com/freebooks/sasp/">Julius O. Smith III: Spectral Audio Signal Processing</a> – free online textbook</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Digital_signal_processing" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Digital_signal_processing" title="Template:Digital signal processing"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Digital_signal_processing" title="Template talk:Digital signal processing"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Digital_signal_processing" title="Special:EditPage/Template:Digital signal processing"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Digital_signal_processing" style="font-size:114%;margin:0 4em"><a href="/wiki/Digital_signal_processing" title="Digital signal processing">Digital signal processing</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theory</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Detection_theory" title="Detection theory">Detection theory</a></li> <li><a href="/wiki/Discrete_time_and_continuous_time" title="Discrete time and continuous time">Discrete signal</a></li> <li><a href="/wiki/Estimation_theory" title="Estimation theory">Estimation theory</a></li> <li><a href="/wiki/Nyquist%E2%80%93Shannon_sampling_theorem" title="Nyquist–Shannon sampling theorem">Nyquist–Shannon sampling theorem</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Sub-fields</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Audio_signal_processing" title="Audio signal processing">Audio signal processing</a></li> <li><a href="/wiki/Digital_image_processing" title="Digital image processing">Digital image processing</a></li> <li><a href="/wiki/Speech_processing" title="Speech processing">Speech processing</a></li> <li><a href="/wiki/Statistical_signal_processing" class="mw-redirect" title="Statistical signal processing">Statistical signal processing</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Techniques</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Z-transform" title="Z-transform">Z-transform</a> <ul><li><a href="/wiki/Advanced_z-transform" title="Advanced z-transform">Advanced z-transform</a></li> <li><a href="/wiki/Matched_Z-transform_method" title="Matched Z-transform method">Matched Z-transform method</a></li></ul></li> <li><a href="/wiki/Bilinear_transform" title="Bilinear transform">Bilinear transform</a></li> <li><a href="/wiki/Constant-Q_transform" title="Constant-Q transform">Constant-Q transform</a></li> <li><a href="/wiki/Discrete_cosine_transform" title="Discrete cosine transform">Discrete cosine transform</a> (DCT)</li> <li><a href="/wiki/Discrete_Fourier_transform" title="Discrete Fourier transform">Discrete Fourier transform</a> (DFT)</li> <li><a href="/wiki/Discrete-time_Fourier_transform" title="Discrete-time Fourier transform">Discrete-time Fourier transform</a> (DTFT)</li> <li><a href="/wiki/Impulse_invariance" title="Impulse invariance">Impulse invariance</a></li> <li><a href="/wiki/Integral_transform" title="Integral transform">Integral transform</a></li> <li><a href="/wiki/Laplace_transform" title="Laplace transform">Laplace transform</a></li> <li><a href="/wiki/Post%27s_inversion_formula" class="mw-redirect" title="Post's inversion formula">Post's inversion formula</a></li> <li><a href="/wiki/Starred_transform" title="Starred transform">Starred transform</a></li> <li><a href="/wiki/Zak_transform" title="Zak transform">Zak transform</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Sampling_(signal_processing)" title="Sampling (signal processing)">Sampling</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aliasing" title="Aliasing">Aliasing</a></li> <li><a href="/wiki/Anti-aliasing_filter" title="Anti-aliasing filter">Anti-aliasing filter</a></li> <li><a href="/wiki/Downsampling_(signal_processing)" title="Downsampling (signal processing)">Downsampling</a></li> <li><a href="/wiki/Nyquist_rate" title="Nyquist rate">Nyquist rate</a> / <a href="/wiki/Nyquist_frequency" title="Nyquist frequency">frequency</a></li> <li><a href="/wiki/Oversampling" title="Oversampling">Oversampling</a></li> <li><a href="/wiki/Quantization_(signal_processing)" title="Quantization (signal processing)">Quantization</a></li> <li><a href="/wiki/Sampling_rate" class="mw-redirect" title="Sampling rate">Sampling rate</a></li> <li><a href="/wiki/Undersampling" title="Undersampling">Undersampling</a></li> <li><a href="/wiki/Upsampling" title="Upsampling">Upsampling</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q208163#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q208163#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="font-size:114%;margin:0 4em"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q208163#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">International</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.worldcat.org/fast/1118281/">FAST</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4054947-1">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85122397">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb119336198">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb119336198">BnF data</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="zpracování signálů"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph135694&CON_LNG=ENG">Czech Republic</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX539079">Spain</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007543871605171">Israel</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/027253287">IdRef</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Signal_processing&oldid=1258826289">https://en.wikipedia.org/w/index.php?title=Signal_processing&oldid=1258826289</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Signal_processing" title="Category:Signal processing">Signal processing</a></li><li><a href="/wiki/Category:Mass_media_technology" title="Category:Mass media technology">Mass media technology</a></li><li><a href="/wiki/Category:Telecommunication_theory" title="Category:Telecommunication theory">Telecommunication theory</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Articles_lacking_in-text_citations_from_January_2017" title="Category:Articles lacking in-text citations from January 2017">Articles lacking in-text citations from January 2017</a></li><li><a href="/wiki/Category:All_articles_lacking_in-text_citations" title="Category:All articles lacking in-text citations">All articles lacking in-text citations</a></li><li><a href="/wiki/Category:Articles_needing_cleanup_from_June_2017" title="Category:Articles needing cleanup from June 2017">Articles needing cleanup from June 2017</a></li><li><a href="/wiki/Category:All_pages_needing_cleanup" title="Category:All pages needing cleanup">All pages needing cleanup</a></li><li><a href="/wiki/Category:Articles_with_sections_that_need_to_be_turned_into_prose_from_June_2017" title="Category:Articles with sections that need to be turned into prose from June 2017">Articles with sections that need to be turned into prose from June 2017</a></li><li><a href="/wiki/Category:Articles_with_multiple_maintenance_issues" title="Category:Articles with multiple maintenance issues">Articles with multiple maintenance issues</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 21 November 2024, at 21:07<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. By using this site, you agree to the <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use" class="extiw" title="foundation:Special:MyLanguage/Policy:Terms of Use">Terms of Use</a> and <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy" class="extiw" title="foundation:Special:MyLanguage/Policy:Privacy policy">Privacy Policy</a>. Wikipedia® is a registered trademark of the <a rel="nofollow" class="external text" href="https://wikimediafoundation.org/">Wikimedia Foundation, Inc.</a>, a non-profit organization.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:General_disclaimer">Disclaimers</a></li> <li id="footer-places-contact"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us">Contact Wikipedia</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/en.wikipedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=Signal_processing&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-f69cdc8f6-rp9p7","wgBackendResponseTime":139,"wgPageParseReport":{"limitreport":{"cputime":"0.583","walltime":"1.351","ppvisitednodes":{"value":2511,"limit":1000000},"postexpandincludesize":{"value":83145,"limit":2097152},"templateargumentsize":{"value":7195,"limit":2097152},"expansiondepth":{"value":18,"limit":100},"expensivefunctioncount":{"value":9,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":111606,"limit":5000000},"entityaccesscount":{"value":1,"limit":400},"timingprofile":["100.00% 675.256 1 -total"," 30.62% 206.739 1 Template:Reflist"," 17.00% 114.826 1 Template:Authority_control"," 13.94% 94.112 20 Template:Cite_book"," 13.63% 92.058 3 Template:Cite_journal"," 12.46% 84.130 1 Template:DSP"," 12.23% 82.607 1 Template:Multiple_issues"," 11.62% 78.480 1 Template:Navbox"," 10.70% 72.261 1 Template:Short_description"," 7.93% 53.558 1 Template:More_footnotes"]},"scribunto":{"limitreport-timeusage":{"value":"0.370","limit":"10.000"},"limitreport-memusage":{"value":6220456,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.canary-84779d6bf6-wgwwp","timestamp":"20241122141235","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Signal processing","url":"https:\/\/en.wikipedia.org\/wiki\/Signal_processing","sameAs":"http:\/\/www.wikidata.org\/entity\/Q208163","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q208163","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2002-02-25T15:51:15Z","dateModified":"2024-11-21T21:07:20Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/1\/11\/Cosine_Series_Plus_Noise.png","headline":"models and analyzes data representations of physical events"}</script> </body> </html>