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class="vector-toc-numb">2</span> <span>Classification</span> </div> </a> <button aria-controls="toc-Classification-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 Classification subsection</span> </button> <ul id="toc-Classification-sublist" class="vector-toc-list"> <li id="toc-Analog_and_digital_signals" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Analog_and_digital_signals"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Analog and digital signals</span> </div> </a> <ul id="toc-Analog_and_digital_signals-sublist" class="vector-toc-list"> <li id="toc-Analog_signal" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Analog_signal"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.1</span> <span>Analog signal</span> </div> </a> <ul id="toc-Analog_signal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Digital_signal" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Digital_signal"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.2</span> <span>Digital signal</span> </div> </a> <ul id="toc-Digital_signal-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Energy_and_power" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Energy_and_power"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Energy and power</span> </div> </a> <ul id="toc-Energy_and_power-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Deterministic_and_random" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Deterministic_and_random"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Deterministic and random</span> </div> </a> <ul id="toc-Deterministic_and_random-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Even_and_odd" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Even_and_odd"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Even and odd</span> </div> </a> <ul id="toc-Even_and_odd-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Periodic" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Periodic"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Periodic</span> </div> </a> <ul id="toc-Periodic-sublist" class="vector-toc-list"> <li id="toc-Time_discretization" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Time_discretization"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5.1</span> <span>Time discretization</span> </div> </a> <ul id="toc-Time_discretization-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Amplitude_quantization" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Amplitude_quantization"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Amplitude quantization</span> </div> </a> <ul id="toc-Amplitude_quantization-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Examples_of_signals" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Examples_of_signals"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Examples of signals</span> </div> </a> <ul id="toc-Examples_of_signals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Signal_processing" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Signal_processing"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Signal processing</span> </div> </a> <ul id="toc-Signal_processing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Signals_and_systems" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Signals_and_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Signals and systems</span> </div> </a> <ul id="toc-Signals_and_systems-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Gallery" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Gallery"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Gallery</span> </div> </a> <ul id="toc-Gallery-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-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-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">9</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">10</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-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</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 56 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-56" 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">56 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/Sein" title="Sein – Afrikaans" lang="af" hreflang="af" data-title="Sein" 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/%D8%A5%D8%B4%D8%A7%D8%B1%D8%A9_(%D8%A7%D8%AA%D8%B5%D8%A7%D9%84%D8%A7%D8%AA)" title="إشارة (اتصالات) – Arabic" lang="ar" hreflang="ar" data-title="إشارة (اتصالات)" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ay mw-list-item"><a href="https://ay.wikipedia.org/wiki/Unancha" title="Unancha – Aymara" lang="ay" hreflang="ay" data-title="Unancha" data-language-autonym="Aymar aru" data-language-local-name="Aymara" class="interlanguage-link-target"><span>Aymar aru</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Siqnal" title="Siqnal – Azerbaijani" lang="az" hreflang="az" data-title="Siqnal" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</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%AF%E0%A7%8B%E0%A6%97%E0%A6%BE%E0%A6%AF%E0%A7%8B%E0%A6%97_%E0%A6%AC%E0%A7%8D%E0%A6%AF%E0%A6%AC%E0%A6%B8%E0%A7%8D%E0%A6%A5%E0%A6%BE)" title="সংকেত (যোগাযোগ ব্যবস্থা) – Bangla" lang="bn" hreflang="bn" data-title="সংকেত (যোগাযোগ ব্যবস্থা)" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%B8%E0%A4%BF%E0%A4%97%E0%A5%8D%E0%A4%A8%E0%A4%B2" title="सिग्नल – Bhojpuri" lang="bh" hreflang="bh" data-title="सिग्नल" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A1%D0%B8%D0%B3%D0%BD%D0%B0%D0%BB" title="Сигнал – Bulgarian" lang="bg" hreflang="bg" data-title="Сигнал" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Signal" title="Signal – Bosnian" lang="bs" hreflang="bs" data-title="Signal" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Senyal_el%C3%A8ctric" title="Senyal elèctric – Catalan" lang="ca" hreflang="ca" data-title="Senyal elèctric" 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" title="Сигнал – Chuvash" lang="cv" hreflang="cv" data-title="Сигнал" 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/Sign%C3%A1l" title="Signál – Czech" lang="cs" hreflang="cs" data-title="Signál" 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/Signal" title="Signal – Danish" lang="da" hreflang="da" data-title="Signal" 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/Elektrisches_Signal" title="Elektrisches Signal – German" lang="de" hreflang="de" data-title="Elektrisches Signal" 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/Signaal_(tehnika)" title="Signaal (tehnika) – Estonian" lang="et" hreflang="et" data-title="Signaal (tehnika)" 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%97%CE%BB%CE%B5%CE%BA%CF%84%CF%81%CE%B9%CE%BA%CF%8C_%CF%83%CE%AE%CE%BC%CE%B1" title="Ηλεκτρικό σήμα – Greek" lang="el" hreflang="el" data-title="Ηλεκτρικό σήμα" 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/Se%C3%B1al_el%C3%A9ctrica" title="Señal eléctrica – Spanish" lang="es" hreflang="es" data-title="Señal eléctrica" 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/Signalo" title="Signalo – Esperanto" lang="eo" hreflang="eo" data-title="Signalo" 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" title="Seinale – Basque" lang="eu" hreflang="eu" data-title="Seinale" 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/%D8%B3%DB%8C%DA%AF%D9%86%D8%A7%D9%84_(%D9%85%D9%87%D9%86%D8%AF%D8%B3%DB%8C_%D8%A8%D8%B1%D9%82)" title="سیگنال (مهندسی برق) – Persian" lang="fa" hreflang="fa" data-title="سیگنال (مهندسی برق)" 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/Signal_%C3%A9lectrique" title="Signal électrique – French" lang="fr" hreflang="fr" data-title="Signal électrique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Sinal" title="Sinal – Galician" lang="gl" hreflang="gl" data-title="Sinal" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</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%A0%84%EC%9E%90%EA%B3%B5%ED%95%99)" title="신호 (전자공학) – Korean" lang="ko" hreflang="ko" data-title="신호 (전자공학)" 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" title="संकेत – Hindi" lang="hi" hreflang="hi" data-title="संकेत" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Elektri%C4%8Dni_signal" title="Električni signal – Croatian" lang="hr" hreflang="hr" data-title="Električni signal" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Sinyal_(elektronika)" title="Sinyal (elektronika) – Indonesian" lang="id" hreflang="id" data-title="Sinyal (elektronika)" 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-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Segnale_elettrico" title="Segnale elettrico – Italian" lang="it" hreflang="it" data-title="Segnale elettrico" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%95%D7%AA_(%D7%AA%D7%A7%D7%A9%D7%95%D7%A8%D7%AA)" title="אות (תקשורת) – Hebrew" lang="he" hreflang="he" data-title="אות (תקשורת)" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A1%D0%B8%D0%B3%D0%BD%D0%B0%D0%BB" title="Сигнал – Kazakh" lang="kk" hreflang="kk" data-title="Сигнал" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A1%D0%B8%D0%B3%D0%BD%D0%B0%D0%BB" title="Сигнал – Kyrgyz" lang="ky" hreflang="ky" data-title="Сигнал" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Signalas" title="Signalas – Lithuanian" lang="lt" hreflang="lt" data-title="Signalas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Isyarat_(kejuruteraan_elektrik)" title="Isyarat (kejuruteraan elektrik) – Malay" lang="ms" hreflang="ms" data-title="Isyarat (kejuruteraan elektrik)" 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-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Signaal_(algemeen)" title="Signaal (algemeen) – Dutch" lang="nl" hreflang="nl" data-title="Signaal (algemeen)" 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_(%E9%9B%BB%E6%B0%97%E5%B7%A5%E5%AD%A6)" title="信号 (電気工学) – Japanese" lang="ja" hreflang="ja" data-title="信号 (電気工学)" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Sygna%C5%82" title="Sygnał – Polish" lang="pl" hreflang="pl" data-title="Sygnał" 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/Sinal_el%C3%A9trico" title="Sinal elétrico – Portuguese" lang="pt" hreflang="pt" data-title="Sinal elétrico" 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/Semnal_(electronic%C4%83)" title="Semnal (electronică) – Romanian" lang="ro" hreflang="ro" data-title="Semnal (electronică)" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Pinchikilla_unancha" title="Pinchikilla unancha – Quechua" lang="qu" hreflang="qu" data-title="Pinchikilla unancha" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D0%B8%D0%B3%D0%BD%D0%B0%D0%BB" title="Сигнал – Russian" lang="ru" hreflang="ru" data-title="Сигнал" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Seegnal" title="Seegnal – Scots" lang="sco" hreflang="sco" data-title="Seegnal" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Sinjalet" title="Sinjalet – Albanian" lang="sq" hreflang="sq" data-title="Sinjalet" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</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%80_(%E0%B6%89%E0%B6%BD%E0%B7%99%E0%B6%9A%E0%B7%8A%E0%B6%A7%E0%B7%8A%E2%80%8D%E0%B6%BB%E0%B7%9C%E0%B6%B1%E0%B7%92%E0%B6%9A_%E0%B7%80%E0%B7%92%E0%B6%AF%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F%E0%B7%80)" title="සංඥාව (ඉලෙක්ට්‍රොනික විද්‍යාව) – Sinhala" lang="si" hreflang="si" data-title="සංඥාව (ඉලෙක්ට්‍රොනික විද්‍යාව)" 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_(electrical_engineering)" title="Signal (electrical engineering) – Simple English" lang="en-simple" hreflang="en-simple" data-title="Signal (electrical engineering)" 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-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Sign%C3%A1l" title="Signál – Slovak" lang="sk" hreflang="sk" data-title="Signál" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Signal" title="Signal – Slovenian" lang="sl" hreflang="sl" data-title="Signal" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Baaq" title="Baaq – Somali" lang="so" hreflang="so" data-title="Baaq" data-language-autonym="Soomaaliga" data-language-local-name="Somali" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%B3%DB%8C%DA%AF%D9%86%D8%A7%DA%B5" title="سیگناڵ – Central Kurdish" lang="ckb" hreflang="ckb" data-title="سیگناڵ" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A1%D0%B8%D0%B3%D0%BD%D0%B0%D0%BB_(%D0%B5%D0%BB%D0%B5%D0%BA%D1%82%D1%80%D0%BE%D1%82%D0%B5%D1%85%D0%BD%D0%B8%D0%BA%D0%B0)" title="Сигнал (електротехника) – Serbian" lang="sr" hreflang="sr" data-title="Сигнал (електротехника)" 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-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Signal" title="Signal – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Signal" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Elektrisk_signal" title="Elektrisk signal – Swedish" lang="sv" hreflang="sv" data-title="Elektrisk signal" 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" title="குறிகை – Tamil" lang="ta" hreflang="ta" data-title="குறிகை" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Sinyal" title="Sinyal – Turkish" lang="tr" hreflang="tr" data-title="Sinyal" 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%A1%D0%B8%D0%B3%D0%BD%D0%B0%D0%BB" title="Сигнал – Ukrainian" lang="uk" hreflang="uk" data-title="Сигнал" 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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"><span class="mw-redirectedfrom">(Redirected from <a href="/w/index.php?title=Signal_(information_theory)&redirect=no" class="mw-redirect" title="Signal (information theory)">Signal (information theory)</a>)</span></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">Varying physical quantity that conveys information</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">For other uses, see <a href="/wiki/Signal_(disambiguation)" class="mw-disambig" title="Signal (disambiguation)">Signal (disambiguation)</a>.</div> <p class="mw-empty-elt"> </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:William_Powell_Frith_The_signal_1858.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/William_Powell_Frith_The_signal_1858.jpg/220px-William_Powell_Frith_The_signal_1858.jpg" decoding="async" width="220" height="264" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/William_Powell_Frith_The_signal_1858.jpg/330px-William_Powell_Frith_The_signal_1858.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/William_Powell_Frith_The_signal_1858.jpg/440px-William_Powell_Frith_The_signal_1858.jpg 2x" data-file-width="2757" data-file-height="3307" /></a><figcaption>In <i>The Signal</i> by <a href="/wiki/William_Powell_Frith" title="William Powell Frith">William Powell Frith</a>, a woman sends a signal by waving a white handkerchief.</figcaption></figure> <p><b>Signal</b> refers to both the process and the result of <a href="/wiki/Signal_transmission" title="Signal transmission">transmission</a> of <a href="/wiki/Data" title="Data">data</a> over some <a href="/wiki/Transmission_media" class="mw-redirect" title="Transmission media">media</a> accomplished by embedding some variation. Signals are important in multiple subject fields including <a href="/wiki/Signal_processing" title="Signal processing">signal processing</a>, <a href="/wiki/Information_theory" title="Information theory">information theory</a> and <a href="/wiki/Biology" title="Biology">biology</a>. </p><p>In signal processing, a signal is a function that conveys <a href="/wiki/Information" title="Information">information</a> about a phenomenon.<sup id="cite_ref-Priemer_1-0" class="reference"><a href="#cite_note-Priemer-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Any quantity that can vary over space or time can be used as a signal to share messages between observers.<sup id="cite_ref-PC_2-0" class="reference"><a href="#cite_note-PC-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> The <i><a href="/wiki/IEEE_Transactions_on_Signal_Processing" title="IEEE Transactions on Signal Processing">IEEE Transactions on Signal Processing</a></i> includes <a href="/wiki/Audio_signal" title="Audio signal">audio</a>, <a href="/wiki/Video" title="Video">video</a>, speech, <a href="/wiki/Image" title="Image">image</a>, <a href="/wiki/Sonar" title="Sonar">sonar</a>, and <a href="/wiki/Radar" title="Radar">radar</a> as examples of signals.<sup id="cite_ref-IEEE_3-0" class="reference"><a href="#cite_note-IEEE-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> A signal may also be defined as <em>any</em> observable change in a quantity over space or time (a <a href="/wiki/Time_series" title="Time series">time series</a>), even if it does not carry information.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> </p><p>In nature, signals can be actions done by an organism to alert other organisms, ranging from the release of plant chemicals to warn nearby plants of a predator, to sounds or motions made by animals to alert other animals of food. Signaling occurs in all organisms even at cellular levels, with <a href="/wiki/Cell_signaling" title="Cell signaling">cell signaling</a>. <a href="/wiki/Signaling_theory" class="mw-redirect" title="Signaling theory">Signaling theory</a>, in <a href="/wiki/Evolutionary_biology" title="Evolutionary biology">evolutionary biology</a>, proposes that a substantial driver for <a href="/wiki/Evolution" title="Evolution">evolution</a> is the ability of animals to communicate with each other by developing ways of signaling. In human engineering, signals are typically provided by a <a href="/wiki/Sensor" title="Sensor">sensor</a>, and often the original form of a signal is converted to another form of energy using a <a href="/wiki/Transducer" title="Transducer">transducer</a>. For example, a <a href="/wiki/Microphone" title="Microphone">microphone</a> converts an acoustic signal to a voltage waveform, and a <a href="/wiki/Loudspeaker" title="Loudspeaker">speaker</a> does the reverse.<sup id="cite_ref-Priemer_1-1" class="reference"><a href="#cite_note-Priemer-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Another important property of a signal is its <a href="/wiki/Entropy_(information_theory)" title="Entropy (information theory)">entropy</a> or <a href="/wiki/Information_content" title="Information content">information content</a>. <a href="/wiki/Information_theory" title="Information theory">Information theory</a> serves as the formal study of signals and their content. The information of a signal is often accompanied by <a href="/wiki/Noise_(electronics)" title="Noise (electronics)">noise</a>, which primarily refers to unwanted modifications of signals, but is often extended to include unwanted signals conflicting with desired signals (<a href="/wiki/Crosstalk" title="Crosstalk">crosstalk</a>). The reduction of noise is covered in part under the heading of <a href="/wiki/Signal_integrity" title="Signal integrity">signal integrity</a>. The separation of desired signals from background noise is the field of <a href="/wiki/Signal_recovery" class="mw-redirect" title="Signal recovery">signal recovery</a>,<sup id="cite_ref-Wilmshurst_6-0" class="reference"><a href="#cite_note-Wilmshurst-6"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> one branch of which is <a href="/wiki/Estimation_theory" title="Estimation theory">estimation theory</a>, a probabilistic approach to suppressing random disturbances. </p><p>Engineering disciplines such as electrical engineering have advanced the design, study, and implementation of systems involving <a href="/wiki/Data_transmission" class="mw-redirect" title="Data transmission">transmission</a>, <a href="/wiki/Data_storage_device" class="mw-redirect" title="Data storage device">storage</a>, and manipulation of information. In the latter half of the 20th century, electrical engineering itself separated into several disciplines: <a href="/wiki/Electronic_engineering" title="Electronic engineering">electronic engineering</a> and <a href="/wiki/Computer_engineering" title="Computer engineering">computer engineering</a> developed to specialize in the design and analysis of systems that manipulate physical signals, while <a href="/wiki/Industrial_design" title="Industrial design">design engineering</a> developed to address the functional design of signals in <a href="/wiki/User_interface" title="User interface">user–machine interfaces</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definitions">Definitions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal&action=edit&section=1" title="Edit section: Definitions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Definitions specific to sub-fields are common: </p> <ul><li>In <a href="/wiki/Electronics" title="Electronics">electronics</a> and <a href="/wiki/Telecommunications" title="Telecommunications">telecommunications</a>, <i>signal</i> refers to any time-varying <a href="/wiki/Voltage" title="Voltage">voltage</a>, <a href="/wiki/Electric_current" title="Electric current">current</a>, or <a href="/wiki/Electromagnetic_wave" class="mw-redirect" title="Electromagnetic wave">electromagnetic wave</a> that carries information.</li> <li>In <a href="/wiki/Signal_processing" title="Signal processing">signal processing</a>, signals are analog and digital representations of analog physical quantities.</li> <li>In <a href="/wiki/Information_theory" title="Information theory">information theory</a>, a signal is a codified message, that is, the sequence of <a href="/wiki/State_variable" title="State variable">states</a> in a <a href="/wiki/Communication_channel" title="Communication channel">communication channel</a> that encodes a message.</li> <li>In a communication system, a <i>transmitter</i> encodes a <i>message</i> to create a signal, which is carried to a <i>receiver</i> by the communication channel. For example, the words "<a href="/wiki/Mary_had_a_little_lamb" class="mw-redirect" title="Mary had a little lamb">Mary had a little lamb</a>" might be the message spoken into a <a href="/wiki/Telephone" title="Telephone">telephone</a>. The telephone transmitter converts the sounds into an electrical signal. The signal is transmitted to the receiving telephone by wires; at the receiver it is reconverted into sounds.</li> <li>In telephone networks, <a href="/wiki/Signaling_(telecommunications)" title="Signaling (telecommunications)">signaling</a>, for example <a href="/wiki/Common-channel_signaling" title="Common-channel signaling">common-channel signaling</a>, refers to phone number and other digital control information rather than the actual voice signal.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Classification">Classification</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal&action=edit&section=2" title="Edit section: Classification"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Signals can be categorized in various ways. The most common<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="The material near this tag needs to be fact-checked with the cited source(s). (March 2022)">verification needed</span></a></i>]</sup> distinction is between discrete and continuous spaces that the functions are defined over, for example, discrete and continuous-time domains. <a href="/wiki/Discrete-time_signal" class="mw-redirect" title="Discrete-time signal">Discrete-time signals</a> are often referred to as <i><a href="/wiki/Time_series" title="Time series">time series</a></i> in other fields. <a href="/wiki/Continuous-time_signal" class="mw-redirect" title="Continuous-time signal">Continuous-time signals</a> are often referred to as <i>continuous signals</i>. </p><p>A second important distinction is between discrete-valued and continuous-valued. Particularly in <a href="/wiki/Digital_signal_processing" title="Digital signal processing">digital signal processing</a>, a <a href="/wiki/Digital_signal_(signal_processing)" title="Digital signal (signal processing)">digital signal</a> may be defined as a sequence of discrete values, typically associated with an underlying continuous-valued physical process. In <a href="/wiki/Digital_electronics" title="Digital electronics">digital electronics</a>, digital signals are the continuous-time waveform signals in a digital system, representing a bit-stream. </p><p>Signals may also be categorized by their spatial distributions as either point source signals (PSSs) or distributed source signals (DSSs).<sup id="cite_ref-PC_2-1" class="reference"><a href="#cite_note-PC-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p><br /> In Signals and Systems, signals can be classified according to many criteria, mainly: according to the different feature of values, classified into <a href="/wiki/Analog_signal" title="Analog signal">analog signals</a> and <a href="/wiki/Digital_signal" title="Digital signal">digital signals</a>; according to the determinacy of signals, classified into deterministic signals and random signals; according to the <a href="/wiki/Signal_strength_in_telecommunications" title="Signal strength in telecommunications">strength of signals</a>, classified into energy signals and power signals. </p> <div class="mw-heading mw-heading3"><h3 id="Analog_and_digital_signals">Analog and digital signals</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal&action=edit&section=3" title="Edit section: Analog and digital signals"><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:Digital-signal-noise.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Digital-signal-noise.svg/220px-Digital-signal-noise.svg.png" decoding="async" width="220" height="133" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Digital-signal-noise.svg/330px-Digital-signal-noise.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Digital-signal-noise.svg/440px-Digital-signal-noise.svg.png 2x" data-file-width="622" data-file-height="376" /></a><figcaption>A digital signal has two or more distinguishable waveforms, in this example, high voltage and low voltages, each of which can be mapped onto a digit. Characteristically, noise can be removed from digital signals provided it is not too extreme.</figcaption></figure> <p>Two main types of signals encountered in practice are <i><a href="/wiki/Analog_signal" title="Analog signal">analog</a></i> and <i><a href="/wiki/Digital_signal" title="Digital signal">digital</a></i>. The figure shows a digital signal that results from approximating an analog signal by its values at particular time instants. Digital signals are <i><a href="/wiki/Quantization_(signal_processing)" title="Quantization (signal processing)">quantized</a></i>, while analog signals are continuous. </p> <div class="mw-heading mw-heading4"><h4 id="Analog_signal">Analog signal</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal&action=edit&section=4" title="Edit section: Analog signal"><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" title="Analog signal">Analog signal</a></div> <p>An analog signal is any <a href="/wiki/Continuous_signal" class="mw-redirect" title="Continuous signal">continuous signal</a> for which the time-varying feature of the signal is a representation of some other time varying quantity, i.e., <i>analogous</i> to another time varying signal. For example, in an analog <a href="/wiki/Audio_signal" title="Audio signal">audio signal</a>, the instantaneous <a href="/wiki/Voltage" title="Voltage">voltage</a> of the signal varies continuously with the <a href="/wiki/Sound_pressure" title="Sound pressure">sound pressure</a>. It differs from a <a href="/wiki/Digital_signal_(signal_processing)" title="Digital signal (signal processing)">digital signal</a>, in which the continuous quantity is a representation of a sequence of <a href="/wiki/Discrete_value" class="mw-redirect" title="Discrete value">discrete values</a> which can only take on one of a finite number of values.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>The term <i>analog signal</i> usually refers to <a href="/wiki/Electrical_signal" class="mw-redirect" title="Electrical signal">electrical signals</a>; however, analog signals may use other mediums such as <a href="/wiki/Classical_mechanics" title="Classical mechanics">mechanical</a>, <a href="/wiki/Pneumatic" class="mw-redirect" title="Pneumatic">pneumatic</a> or <a href="/wiki/Hydraulic" class="mw-redirect" title="Hydraulic">hydraulic</a>. An analog signal uses some property of the medium to convey the signal's information. For example, an <a href="/wiki/Aneroid_barometer" class="mw-redirect" title="Aneroid barometer">aneroid barometer</a> uses rotary position as the signal to convey pressure information. In an electrical signal, the <a href="/wiki/Voltage" title="Voltage">voltage</a>, <a href="/wiki/Electric_current" title="Electric current">current</a>, or <a href="/wiki/Frequency" title="Frequency">frequency</a> of the signal may be varied to represent the information. </p><p>Any information may be conveyed by an analog signal; often such a signal is a measured response to changes in physical phenomena, such as <a href="/wiki/Sound" title="Sound">sound</a>, <a href="/wiki/Light" title="Light">light</a>, <a href="/wiki/Temperature" title="Temperature">temperature</a>, position, or <a href="/wiki/Pressure" title="Pressure">pressure</a>. The physical variable is converted to an analog signal by a <a href="/wiki/Transducer" title="Transducer">transducer</a>. For example, in sound recording, fluctuations in air pressure (that is to say, <a href="/wiki/Sound" title="Sound">sound</a>) strike the diaphragm of a <a href="/wiki/Microphone" title="Microphone">microphone</a> which induces corresponding electrical fluctuations. The voltage or the current is said to be an <i>analog</i> of the sound. </p> <div class="mw-heading mw-heading4"><h4 id="Digital_signal">Digital signal</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal&action=edit&section=5" title="Edit section: Digital signal"><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" title="Digital signal">Digital signal</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Original_message.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Original_message.jpg/220px-Original_message.jpg" decoding="async" width="220" height="36" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Original_message.jpg/330px-Original_message.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/c/cf/Original_message.jpg 2x" data-file-width="435" data-file-height="72" /></a><figcaption>A binary signal, also known as a logic signal, is a digital signal with two distinguishable levels</figcaption></figure> <p>A digital signal is a signal that is constructed from a discrete set of <a href="/wiki/Waveform" title="Waveform">waveforms</a> of a physical quantity so as to represent a sequence of <a href="/wiki/Discrete_space" title="Discrete space">discrete</a> values.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-waveform_11-0" class="reference"><a href="#cite_note-waveform-11"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> A <i>logic signal</i> is a digital signal with only two possible values,<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> and describes an arbitrary <a href="/wiki/Bit_stream" class="mw-redirect" title="Bit stream">bit stream</a>. Other types of digital signals can represent <a href="/wiki/Three-valued_logic" title="Three-valued logic">three-valued logic</a> or higher valued logics. </p><p>Alternatively, a digital signal may be considered to be the sequence of codes represented by such a physical quantity.<sup id="cite_ref-Khanna_14-0" class="reference"><a href="#cite_note-Khanna-14"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> The physical quantity may be a variable electric current or voltage, the intensity, phase or <a href="/wiki/Polarization_(waves)" title="Polarization (waves)">polarization</a> of an <a href="/wiki/Optical" class="mw-redirect" title="Optical">optical</a> or other <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetic field</a>, acoustic pressure, the <a href="/wiki/Magnetization" title="Magnetization">magnetization</a> of a <a href="/wiki/Magnetic_storage" title="Magnetic storage">magnetic storage</a> media, etc. Digital signals are present in all <a href="/wiki/Digital_electronics" title="Digital electronics">digital electronics</a>, notably computing equipment and <a href="/wiki/Data_transmission" class="mw-redirect" title="Data transmission">data transmission</a>. </p><p>With digital signals, system noise, provided it is not too great, will not affect system operation whereas noise always degrades the operation of <a href="/wiki/Analog_signals" class="mw-redirect" title="Analog signals">analog signals</a> to some degree. </p><p>Digital signals often arise via <a href="/wiki/Sampling_(signal_processing)" title="Sampling (signal processing)">sampling</a> of analog signals, for example, a continually fluctuating voltage on a line that can be digitized by an <a href="/wiki/Analog-to-digital_converter" title="Analog-to-digital converter">analog-to-digital converter</a> circuit, wherein the circuit will read the voltage level on the line, say, every 50 <a href="/wiki/Microseconds" class="mw-redirect" title="Microseconds">microseconds</a> and represent each reading with a fixed number of bits. The resulting stream of numbers is stored as digital data on a discrete-time and quantized-amplitude signal. <a href="/wiki/Computer" title="Computer">Computers</a> and other <a href="/wiki/Digital_data" title="Digital data">digital</a> devices are restricted to discrete time. </p> <div class="mw-heading mw-heading3"><h3 id="Energy_and_power">Energy and power</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal&action=edit&section=6" title="Edit section: Energy and power"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>According to the strengths of signals, practical signals can be classified into two categories: energy signals and power signals.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p>Energy signals: Those signals' <a href="/wiki/Energy" title="Energy">energy</a> are equal to a finite positive value, but their average powers are 0; </p><p><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 0<E=\int _{-\infty }^{\infty }s^{2}(t)dt<\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo><</mo> <mi>E</mi> <mo>=</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>t</mi> <mo><</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0<E=\int _{-\infty }^{\infty }s^{2}(t)dt<\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fce0b4cfe3df4250c486c1c1e17fd8b6dd44c517" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:26.24ex; height:6.009ex;" alt="{\displaystyle 0<E=\int _{-\infty }^{\infty }s^{2}(t)dt<\infty }"></span> </p><p>Power signals: Those signals' average <a href="/wiki/Power_(physics)" title="Power (physics)">power</a> are equal to a finite <a href="/wiki/Sign_(mathematics)" title="Sign (mathematics)">positive</a> value, but their energy are <a href="/wiki/Infinity" title="Infinity">infinite</a>. </p><p><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 P=\lim _{T\rightarrow \infty }{\frac {1}{T}}\int _{-T/2}^{T/2}s^{2}(t)dt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>T</mi> </mfrac> </mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msubsup> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P=\lim _{T\rightarrow \infty }{\frac {1}{T}}\int _{-T/2}^{T/2}s^{2}(t)dt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e155e0986151e0e22e436b48b973307d51ab531d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:25.374ex; height:6.676ex;" alt="{\displaystyle P=\lim _{T\rightarrow \infty }{\frac {1}{T}}\int _{-T/2}^{T/2}s^{2}(t)dt}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Deterministic_and_random">Deterministic and random</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal&action=edit&section=7" title="Edit section: Deterministic and random"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Deterministic signals are those whose values at any time are predictable and can be calculated by a mathematical equation. </p><p>Random signals are signals that take on random values at any given time instant and must be modeled <a href="/wiki/Stochastic" title="Stochastic">stochastically</a>.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Even_and_odd">Even and odd</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal&action=edit&section=8" title="Edit section: Even and odd"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <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="theader">Even and odd signals</div></div><div class="trow"><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Function_x%5E2.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Function_x%5E2.svg/200px-Function_x%5E2.svg.png" decoding="async" width="200" height="222" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Function_x%5E2.svg/300px-Function_x%5E2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/dd/Function_x%5E2.svg/400px-Function_x%5E2.svg.png 2x" data-file-width="900" data-file-height="1000" /></a></span></div><div class="thumbcaption"><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 f(x)=x^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)=x^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84ddac4ae10b1aa4a11741c79771a583419fb1fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.9ex; height:3.176ex;" alt="{\displaystyle f(x)=x^{2}}"></span> is an example of an even signal.</div></div><div class="tsingle" style="width:202px;max-width:202px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Function_x%5E3.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Function_x%5E3.svg/200px-Function_x%5E3.svg.png" decoding="async" width="200" height="219" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Function_x%5E3.svg/300px-Function_x%5E3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f5/Function_x%5E3.svg/400px-Function_x%5E3.svg.png 2x" data-file-width="912" data-file-height="1000" /></a></span></div><div class="thumbcaption"><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 f(x)=x^{3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)=x^{3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b666f585570f17a4015f8bc1797a8c074744d27" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.9ex; height:3.176ex;" alt="{\displaystyle f(x)=x^{3}}"></span> is an example of an odd signal.</div></div></div></div></div> <p>An <a href="/wiki/Even_and_odd_functions" title="Even and odd functions">even signal</a> satisfies the condition <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)=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> <mo>=</mo> <mi>x</mi> <mo stretchy="false">(</mo> <mo>−</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x(t)=x(-t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c00fd52d227b5b4d89bf7d0f821af383507ac0a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.864ex; height:2.843ex;" alt="{\displaystyle x(t)=x(-t)}"></span> </p><p>or equivalently if the following equation holds for all <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 t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> and <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 -t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/198aea65d6b8a474eebd6271c9499a3d92096bdb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:2.648ex; height:2.176ex;" alt="{\displaystyle -t}"></span> in the domain of <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span>: </p> <dl><dd><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)-x(-t)=0.}"> <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> <mo>−</mo> <mi>x</mi> <mo stretchy="false">(</mo> <mo>−</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x(t)-x(-t)=0.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a7fa0c52b8321de2b425bd21be01f814dea7921" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.513ex; height:2.843ex;" alt="{\displaystyle x(t)-x(-t)=0.}"></span></dd></dl> <p>An odd signal satisfies the condition <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)=-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> <mo>=</mo> <mo>−</mo> <mi>x</mi> <mo stretchy="false">(</mo> <mo>−</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x(t)=-x(-t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0eee51ae51dea7b5b6ceae4d50a47aa06a9c921a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.672ex; height:2.843ex;" alt="{\displaystyle x(t)=-x(-t)}"></span> </p><p>or equivalently if the following equation holds for all <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 t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.84ex; height:2.009ex;" alt="{\displaystyle t}"></span> and <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 -t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/198aea65d6b8a474eebd6271c9499a3d92096bdb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:2.648ex; height:2.176ex;" alt="{\displaystyle -t}"></span> in the domain of <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span>: </p> <dl><dd><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)+x(-t)=0.}"> <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> <mo>+</mo> <mi>x</mi> <mo stretchy="false">(</mo> <mo>−</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x(t)+x(-t)=0.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99b1816a0d38386298ec9fc42a6c62912d5dd671" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.513ex; height:2.843ex;" alt="{\displaystyle x(t)+x(-t)=0.}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Periodic">Periodic</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal&action=edit&section=9" title="Edit section: Periodic"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A signal is said to be <a href="/wiki/Periodic_function" title="Periodic function">periodic</a> if it satisfies the condition: </p><p><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)=x(t+T)\quad \forall t\in [t_{0},t_{max}]}"> <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> <mo>=</mo> <mi>x</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo>+</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mspace width="1em" /> <mi mathvariant="normal">∀</mi> <mi>t</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x(t)=x(t+T)\quad \forall t\in [t_{0},t_{max}]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e7a8ab47f7f95ddc48458ad015914817fb2bdea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:31.374ex; height:2.843ex;" alt="{\displaystyle x(t)=x(t+T)\quad \forall t\in [t_{0},t_{max}]}"></span> or <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(n)=x(n+N)\quad \forall n\in [n_{0},n_{max}]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>x</mi> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mi>N</mi> <mo stretchy="false">)</mo> <mspace width="1em" /> <mi mathvariant="normal">∀</mi> <mi>n</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x(n)=x(n+N)\quad \forall n\in [n_{0},n_{max}]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/39c57e4c74c602caa13e4984a7b867260f09127c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:34.577ex; height:2.843ex;" alt="{\displaystyle x(n)=x(n+N)\quad \forall n\in [n_{0},n_{max}]}"></span> </p><p>Where: </p><p><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 T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> = fundamental time <a href="/wiki/Period_(physics)" class="mw-redirect" title="Period (physics)">period</a>, </p><p><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 1/T=f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>T</mi> <mo>=</mo> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1/T=f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef8a273a63df8ea327d14bae037f350422559b31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.338ex; height:2.843ex;" alt="{\displaystyle 1/T=f}"></span>= fundamental <a href="/wiki/Frequency" title="Frequency">frequency</a>. </p><p>The same can be applied to <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 N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span>. A periodic signal will repeat for every period. </p> <div class="mw-heading mw-heading4"><h4 id="Time_discretization">Time discretization<span class="anchor" id="Discretization"></span></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal&action=edit&section=10" title="Edit section: Time discretization"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Sampled.signal.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Sampled.signal.svg/220px-Sampled.signal.svg.png" decoding="async" width="220" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Sampled.signal.svg/330px-Sampled.signal.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/88/Sampled.signal.svg/440px-Sampled.signal.svg.png 2x" data-file-width="585" data-file-height="330" /></a><figcaption>Discrete-time signal created from a continuous signal by <a href="/wiki/Sampling_(signal_processing)" title="Sampling (signal processing)">sampling</a></figcaption></figure> <p>Signals can be classified as <a href="/wiki/Continuous_signal" class="mw-redirect" title="Continuous signal">continuous</a> or <a href="/wiki/Discrete_time" class="mw-redirect" title="Discrete time">discrete time</a>. In the mathematical abstraction, the domain of a continuous-time signal is the set of real numbers (or some interval thereof), whereas the domain of a discrete-time (DT) signal is the set of <a href="/wiki/Integer" title="Integer">integers</a> (or other subsets of real numbers). What these integers represent depends on the nature of the signal; most often it is time. </p><p>A continuous-time signal is any <a href="/wiki/Mathematical_function" class="mw-redirect" title="Mathematical function">function</a> which is defined at every time <i>t</i> in an interval, most commonly an infinite interval. A simple source for a discrete-time signal is the <a href="/wiki/Sampling_(signal_processing)" title="Sampling (signal processing)">sampling</a> of a continuous signal, approximating the signal by a sequence of its values at particular time instants. </p> <div class="mw-heading mw-heading3"><h3 id="Amplitude_quantization">Amplitude quantization<span class="anchor" id="Quantization"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal&action=edit&section=11" title="Edit section: Amplitude quantization"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>If a signal is to be represented as a sequence of digital data, it is impossible to maintain exact precision – each number in the sequence must have a finite number of digits. As a result, the values of such a signal must be <a href="/wiki/Quantization_(signal_processing)" title="Quantization (signal processing)">quantized</a> into a <a href="/wiki/Finite_set" title="Finite set">finite set</a> for practical representation. Quantization is the process of converting a continuous analog audio signal to a digital signal with discrete numerical values of integers. </p> <div class="mw-heading mw-heading2"><h2 id="Examples_of_signals">Examples of signals</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal&action=edit&section=12" title="Edit section: Examples of signals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Naturally occurring signals can be converted to electronic signals by various <a href="/wiki/Sensor" title="Sensor">sensors</a>. Examples include: </p> <ul><li><i><a href="/wiki/Motion" title="Motion">Motion</a></i>. The motion of an object can be considered to be a signal and can be monitored by various sensors to provide electrical signals.<sup id="cite_ref-Lu_17-0" class="reference"><a href="#cite_note-Lu-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> For example, <a href="/wiki/Radar" title="Radar">radar</a> can provide an electromagnetic signal for following aircraft motion. A motion signal is one-dimensional (time), and the range is generally three-dimensional. Position is thus a 3-vector signal; position and orientation of a rigid body is a 6-vector signal. Orientation signals can be generated using a <a href="/wiki/Gyroscope" title="Gyroscope">gyroscope</a>.<sup id="cite_ref-gyro_18-0" class="reference"><a href="#cite_note-gyro-18"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup></li> <li><i><a href="/wiki/Sound" title="Sound">Sound</a></i>. Since a sound is a <a href="/wiki/Oscillation" title="Oscillation">vibration</a> of a medium (such as air), a sound signal associates a <a href="/wiki/Pressure" title="Pressure">pressure</a> value to every value of time and possibly three space coordinates indicating the direction of travel. A sound signal is converted to an electrical signal by a <a href="/wiki/Microphone" title="Microphone">microphone</a>, generating a <a href="/wiki/Voltage" title="Voltage">voltage</a> signal as an analog of the sound signal. Sound signals can be <a href="/wiki/Sampling_(signal_processing)" title="Sampling (signal processing)">sampled</a> at a discrete set of time points; for example, <a href="/wiki/Compact_disc" title="Compact disc">compact discs</a> (CDs) contain discrete signals representing sound, recorded at <a href="/wiki/44,100_Hz" title="44,100 Hz">44,100 Hz</a>; since CDs are recorded in <a href="/wiki/Stereo" class="mw-redirect" title="Stereo">stereo</a>, each sample contains data for a left and right channel, which may be considered to be a 2-vector signal. The CD encoding is converted to an electrical signal by reading the information with a <a href="/wiki/Laser" title="Laser">laser</a>, converting the sound signal to an optical signal.<sup id="cite_ref-Chambers_19-0" class="reference"><a href="#cite_note-Chambers-19"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup></li> <li><i><a href="/wiki/Image" title="Image">Images</a></i>. A picture or image consists of a brightness or color signal, a function of a two-dimensional location. The object's appearance is presented as emitted or reflected <a href="/wiki/Light" title="Light">light</a>, an electromagnetic signal. It can be converted to voltage or current waveforms using devices such as the <a href="/wiki/Charge-coupled_device" title="Charge-coupled device">charge-coupled device</a>. A 2D image can have a continuous spatial domain, as in a traditional photograph or painting; or the image can be discretized in space, as in a <a href="/wiki/Digital_image" title="Digital image">digital image</a>. Color images are typically represented as a combination of monochrome images in three <a href="/wiki/Primary_colors" class="mw-redirect" title="Primary colors">primary colors</a>.</li> <li><i><a href="/wiki/Video" title="Video">Videos</a></i>. A video signal is a sequence of images. A point in a video is identified by its two-dimensional position in the image and by the time at which it occurs, so a video signal has a three-dimensional domain. Analog video has one continuous domain dimension (across a <a href="/wiki/Scan_line" title="Scan line">scan line</a>) and two discrete dimensions (frame and line).</li> <li>Biological <i><a href="/wiki/Membrane_potential" title="Membrane potential">membrane potentials</a></i>. The value of the signal is an <a href="/wiki/Electric_potential" title="Electric potential">electric potential</a> (voltage). The domain is more difficult to establish. Some <a href="/wiki/Cell_(biology)" title="Cell (biology)">cells</a> or <a href="/wiki/Organelle" title="Organelle">organelles</a> have the same membrane potential throughout; <a href="/wiki/Neuron" title="Neuron">neurons</a> generally have different potentials at different points. These signals have very low energies, but are enough to make nervous systems work; they can be measured in aggregate by <a href="/wiki/Electrophysiology" title="Electrophysiology">electrophysiology</a> techniques.</li> <li>The output of a <a href="/wiki/Thermocouple" title="Thermocouple">thermocouple</a>, which conveys temperature information.<sup id="cite_ref-Priemer_1-2" class="reference"><a href="#cite_note-Priemer-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></li> <li>The output of a <a href="/wiki/PH_meter" title="PH meter">pH meter</a> which conveys acidity information.<sup id="cite_ref-Priemer_1-3" class="reference"><a href="#cite_note-Priemer-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Signal_processing">Signal processing</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal&action=edit&section=13" title="Edit section: Signal processing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <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 signals</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Signal_processing" title="Signal processing">Signal processing</a></div> <p>Signal processing is the manipulation of signals. A common example is signal transmission between different locations. The embodiment of a signal in electrical form is made by a <a href="/wiki/Transducer" title="Transducer">transducer</a> that converts the signal from its original form to a <a href="/wiki/Waveform" title="Waveform">waveform</a> expressed as a <a href="/wiki/Electric_current" title="Electric current">current</a> or a <a href="/wiki/Voltage" title="Voltage">voltage</a>, or <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic radiation</a>, for example, an <a href="/wiki/Free-space_optical_communication" title="Free-space optical communication">optical signal</a> or <a href="/wiki/Radio_transmission" class="mw-redirect" title="Radio transmission">radio transmission</a>. Once expressed as an electronic signal, the signal is available for further processing by electrical devices such as <a href="/wiki/Electronic_amplifier" class="mw-redirect" title="Electronic amplifier">electronic amplifiers</a> and <a href="/wiki/Electronic_filters" class="mw-redirect" title="Electronic filters">filters</a>, and can be transmitted to a remote location by a <a href="/wiki/Transmitter" title="Transmitter">transmitter</a> and received using <a href="/wiki/Radio_receiver" title="Radio receiver">radio receivers</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Signals_and_systems">Signals and systems</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal&action=edit&section=14" title="Edit section: Signals and systems"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Electrical_engineering" title="Electrical engineering">electrical engineering</a> (EE) programs, signals are covered in a class and field of study known as <i>signals and systems</i>. Depending on the school, undergraduate EE students generally take the class as juniors or seniors, normally depending on the number and level of previous <a href="/wiki/Linear_algebra" title="Linear algebra">linear algebra</a> and <a href="/wiki/Differential_equation" title="Differential equation">differential equation</a> classes they have taken.<sup id="cite_ref-McMahon_s_and_s_20-0" class="reference"><a href="#cite_note-McMahon_s_and_s-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>The field studies input and output signals, and the mathematical representations between them known as systems, in four domains: time, frequency, <i>s</i> and <i>z</i>. Since signals and systems are both studied in these four domains, there are 8 major divisions of study. As an example, when working with continuous-time signals (<i>t</i>), one might transform from the time domain to a frequency or <i>s</i> domain; or from discrete time (<i>n</i>) to frequency or <i>z</i> domains. Systems also can be transformed between these domains like signals, with continuous to <i>s</i> and discrete to <i>z</i>. </p><p>Signals and systems is a subset of the field of <a href="/wiki/Mathematical_model" title="Mathematical model">mathematical modeling</a>. It involves circuit analysis and design via mathematical modeling and some numerical methods, and was updated several decades ago with <a href="/wiki/Dynamical_system" title="Dynamical system">dynamical systems</a> tools including differential equations, and recently, <a href="/wiki/Lagrangian_mechanics" title="Lagrangian mechanics">Lagrangians</a>. Students are expected to understand the modeling tools as well as the mathematics, physics, circuit analysis, and transformations between the 8 domains. </p><p>Because mechanical engineering (ME) topics like friction, dampening etc. have very close analogies in signal science (inductance, resistance, voltage, etc.), many of the tools originally used in ME transformations (Laplace and Fourier transforms, Lagrangians, sampling theory, probability, difference equations, etc.) have now been applied to signals, circuits, systems and their components, analysis and design in EE. Dynamical systems that involve noise, filtering and other random or chaotic attractors and repellers have now placed stochastic sciences and statistics between the more deterministic discrete and continuous functions in the field. (Deterministic as used here means signals that are completely determined as functions of time). </p><p>EE taxonomists are still not decided where signals and systems falls within the whole field of signal processing vs. circuit analysis and mathematical modeling, but the common link of the topics that are covered in the course of study has brightened boundaries with dozens of books, journals, etc. called "Signals and Systems", and used as text and test prep for the EE, as well as, recently, computer engineering exams.<sup id="cite_ref-Signals_and_systems_21-0" class="reference"><a href="#cite_note-Signals_and_systems-21"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Gallery">Gallery</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal&action=edit&section=15" title="Edit section: Gallery"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul class="gallery mw-gallery-traditional" style="max-width: 772px;"> <li class="gallerybox" style="width: 185px"> <div class="thumb" style="width: 180px; height: 180px;"><span typeof="mw:File"><a href="/wiki/File:Signalman_sends_semaphore_message_from_Pearl_Harbor_Control_Tower_c1960.jpg" class="mw-file-description" title="A signalman sends a semaphore message from a Pearl Harbor Control Tower, c. 1960."><img alt="A signalman sends a semaphore message from a Pearl Harbor Control Tower, c. 1960." src="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Signalman_sends_semaphore_message_from_Pearl_Harbor_Control_Tower_c1960.jpg/150px-Signalman_sends_semaphore_message_from_Pearl_Harbor_Control_Tower_c1960.jpg" decoding="async" width="150" height="113" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Signalman_sends_semaphore_message_from_Pearl_Harbor_Control_Tower_c1960.jpg/225px-Signalman_sends_semaphore_message_from_Pearl_Harbor_Control_Tower_c1960.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/88/Signalman_sends_semaphore_message_from_Pearl_Harbor_Control_Tower_c1960.jpg/300px-Signalman_sends_semaphore_message_from_Pearl_Harbor_Control_Tower_c1960.jpg 2x" data-file-width="616" data-file-height="462" /></a></span></div> <div class="gallerytext">A signalman sends a semaphore message from a Pearl Harbor Control Tower, <abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 1960</span>.</div> </li> <li class="gallerybox" style="width: 185px"> <div class="thumb" style="width: 180px; height: 180px;"><span typeof="mw:File"><a href="/wiki/File:Finnish_distant_signal_displaying_Expect_Stop.jpg" class="mw-file-description" title="A Finnish distant signal at the western approach to Muhos station is displaying Expect Stop."><img alt="A Finnish distant signal at the western approach to Muhos station is displaying Expect Stop." src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Finnish_distant_signal_displaying_Expect_Stop.jpg/105px-Finnish_distant_signal_displaying_Expect_Stop.jpg" decoding="async" width="105" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Finnish_distant_signal_displaying_Expect_Stop.jpg/158px-Finnish_distant_signal_displaying_Expect_Stop.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e5/Finnish_distant_signal_displaying_Expect_Stop.jpg/211px-Finnish_distant_signal_displaying_Expect_Stop.jpg 2x" data-file-width="230" data-file-height="327" /></a></span></div> <div class="gallerytext">A Finnish distant signal at the western approach to <a href="/wiki/Muhos" title="Muhos">Muhos</a> station is displaying <i>Expect Stop</i>.</div> </li> <li class="gallerybox" style="width: 185px"> <div class="thumb" style="width: 180px; height: 180px;"><span typeof="mw:File"><a href="/wiki/File:Hailing_a_cab.jpg" class="mw-file-description" title="A woman hailing a cab is sending a signal of availability to be picked up."><img alt="A woman hailing a cab is sending a signal of availability to be picked up." src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Hailing_a_cab.jpg/150px-Hailing_a_cab.jpg" decoding="async" width="150" height="100" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Hailing_a_cab.jpg/225px-Hailing_a_cab.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Hailing_a_cab.jpg/300px-Hailing_a_cab.jpg 2x" data-file-width="2592" data-file-height="1728" /></a></span></div> <div class="gallerytext">A woman hailing a cab is sending a signal of availability to be picked up.</div> </li> <li class="gallerybox" style="width: 185px"> <div class="thumb" style="width: 180px; height: 180px;"><span typeof="mw:File"><a href="/wiki/File:Signal_flare_during_a_rescue_training_mission.jpg" class="mw-file-description" title="A flare is a common means to signal during dark or smoke-filled conditions."><img alt="A flare is a common means to signal during dark or smoke-filled conditions." src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Signal_flare_during_a_rescue_training_mission.jpg/108px-Signal_flare_during_a_rescue_training_mission.jpg" decoding="async" width="108" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Signal_flare_during_a_rescue_training_mission.jpg/162px-Signal_flare_during_a_rescue_training_mission.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Signal_flare_during_a_rescue_training_mission.jpg/217px-Signal_flare_during_a_rescue_training_mission.jpg 2x" data-file-width="1517" data-file-height="2100" /></a></span></div> <div class="gallerytext">A <a href="/wiki/Flare" title="Flare">flare</a> is a common means to signal during dark or smoke-filled conditions.</div> </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&action=edit&section=16" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/40px-Wikibooks-logo-en-noslogan.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/60px-Wikibooks-logo-en-noslogan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/80px-Wikibooks-logo-en-noslogan.svg.png 2x" data-file-width="400" data-file-height="400" /></span></span></div> <div class="side-box-text plainlist">Wikibooks has a book on the topic of: <i><b><a href="https://en.wikibooks.org/wiki/Signals_and_Systems" class="extiw" title="wikibooks:Signals and Systems">Signals and Systems</a></b></i></div></div> </div> <ul><li><a href="/wiki/A_Mathematical_Theory_of_Communication" title="A Mathematical Theory of Communication">A Mathematical Theory of Communication</a> – 1948 scholarly article by Claude Shannon</li> <li><a href="/wiki/Current_loop" title="Current loop">Current loop</a> – a signaling system in widespread use for process control</li> <li><a href="/wiki/Signal-to-noise_ratio" title="Signal-to-noise ratio">Signal-to-noise ratio</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal&action=edit&section=17" title="Edit section: Notes"><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 reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Some authors do not emphasize the role of information in the definition of a signal.<sup id="cite_ref-Sinha_4-0" class="reference"><a href="#cite_note-Sinha-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></span> </li> </ol></div></div> <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&action=edit&section=18" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-Priemer-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Priemer_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Priemer_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Priemer_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Priemer_1-3"><sup><i><b>d</b></i></sup></a></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="CITEREFRoland_Priemer1991" class="citation book cs1">Roland Priemer (1991). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=QBT7nP7zTLgC&pg=PA1"><i>Introductory Signal Processing</i></a>. World Scientific. p. 1. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-9971509194" title="Special:BookSources/978-9971509194"><bdi>978-9971509194</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130602161539/http://books.google.com/books?id=QBT7nP7zTLgC&pg=PA1">Archived</a> from the original on 2013-06-02. <q>A signal is a function that conveys information about the behavior of a system or attributes of some phenomenon.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introductory+Signal+Processing&rft.pages=1&rft.pub=World+Scientific&rft.date=1991&rft.isbn=978-9971509194&rft.au=Roland+Priemer&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DQBT7nP7zTLgC%26pg%3DPA1&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" class="Z3988"></span></span> </li> <li id="cite_note-PC-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-PC_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-PC_2-1"><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="CITEREFChakravorty2018" class="citation journal cs1">Chakravorty, Pragnan (2018). "What Is a Signal? [Lecture Notes]". <i>IEEE Signal Processing Magazine</i>. <b>35</b> (5): 175–177. <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/2018ISPM...35e.175C">2018ISPM...35e.175C</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%2FMSP.2018.2832195">10.1109/MSP.2018.2832195</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:52164353">52164353</a>. <q>Consequently, a signal, represented as a function of one or more variables, may be defined as an observable change in a quantifiable entity.</q></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=What+Is+a+Signal%3F+%5BLecture+Notes%5D&rft.volume=35&rft.issue=5&rft.pages=175-177&rft.date=2018&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A52164353%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FMSP.2018.2832195&rft_id=info%3Abibcode%2F2018ISPM...35e.175C&rft.aulast=Chakravorty&rft.aufirst=Pragnan&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" class="Z3988"></span></span> </li> <li id="cite_note-IEEE-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-IEEE_3-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1"><a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78">"Aims and scope"</a>. <i>IEEE Transactions on Signal Processing</i>. <a href="/wiki/IEEE" class="mw-redirect" title="IEEE">IEEE</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120417233106/http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78">Archived</a> from the original on 2012-04-17.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Signal+Processing&rft.atitle=Aims+and+scope&rft_id=https%3A%2F%2Fieeexplore.ieee.org%2Fxpl%2FRecentIssue.jsp%3Fpunumber%3D78&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" class="Z3988"></span></span> </li> <li id="cite_note-Sinha-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Sinha_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPriyabrata_Sinha2009" class="citation book cs1">Priyabrata Sinha (2009). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=mrOHsYChY-oC&pg=PA9"><i>Speech processing in embedded systems</i></a>. Springer. p. 9. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0387755809" title="Special:BookSources/978-0387755809"><bdi>978-0387755809</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130602161013/http://books.google.com/books?id=mrOHsYChY-oC&pg=PA9">Archived</a> from the original on 2013-06-02. <q>To put it very generally, a signal is any time-varying physical quantity.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Speech+processing+in+embedded+systems&rft.pages=9&rft.pub=Springer&rft.date=2009&rft.isbn=978-0387755809&rft.au=Priyabrata+Sinha&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DmrOHsYChY-oC%26pg%3DPA9&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" class="Z3988"></span></span> </li> <li id="cite_note-Wilmshurst-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Wilmshurst_6-0">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFT._H._Wilmshurst1990" class="citation book cs1">T. H. Wilmshurst (1990). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=49hfsIPpGwYC&pg=PP11"><i>Signal Recovery from Noise in Electronic Instrumentation</i></a> (2nd ed.). CRC Press. pp. 11 <i>ff</i>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0750300582" title="Special:BookSources/978-0750300582"><bdi>978-0750300582</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150319012552/http://books.google.com/books?id=49hfsIPpGwYC&pg=PP11">Archived</a> from the original on 2015-03-19.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Signal+Recovery+from+Noise+in+Electronic+Instrumentation&rft.pages=11+%27%27ff%27%27&rft.edition=2nd&rft.pub=CRC+Press&rft.date=1990&rft.isbn=978-0750300582&rft.au=T.+H.+Wilmshurst&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D49hfsIPpGwYC%26pg%3DPP11&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" class="Z3988"></span></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://www.st-andrews.ac.uk/~www_pa/Scots_Guide/info/signals/digital/digital.htm">"Digital signals"</a>. <i>www.st-andrews.ac.uk</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170302055200/http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/info/signals/digital/digital.htm">Archived</a> from the original on 2017-03-02<span class="reference-accessdate">. Retrieved <span class="nowrap">2017-12-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.st-andrews.ac.uk&rft.atitle=Digital+signals&rft_id=https%3A%2F%2Fwww.st-andrews.ac.uk%2F~www_pa%2FScots_Guide%2Finfo%2Fsignals%2Fdigital%2Fdigital.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</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://learn.sparkfun.com/tutorials/analog-vs-digital/digital-signals">"Analog vs. Digital - learn.sparkfun.com"</a>. <i>learn.sparkfun.com</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170705100418/https://learn.sparkfun.com/tutorials/analog-vs-digital/digital-signals">Archived</a> from the original on 2017-07-05<span class="reference-accessdate">. Retrieved <span class="nowrap">2017-12-17</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=learn.sparkfun.com&rft.atitle=Analog+vs.+Digital+-+learn.sparkfun.com&rft_id=https%3A%2F%2Flearn.sparkfun.com%2Ftutorials%2Fanalog-vs-digital%2Fdigital-signals&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRobert_K._Dueck2005" class="citation book cs1">Robert K. Dueck (2005). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20171217234501/https://books.google.com/books?id=1eO7kLWUmYIC&lpg=PA49&ots=EBhxEwk7bY&dq=digital%20signal%20logic&pg=PA4"><i>Digital Design with CPLD Applications and VHDL</i></a>. Thomson/Delmar Learning. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1401840302" title="Special:BookSources/1401840302"><bdi>1401840302</bdi></a>. Archived from <a rel="nofollow" class="external text" href="https://books.google.com/books?id=1eO7kLWUmYIC&q=digital%20signal%20logic&pg=PA4">the original</a> on 2017-12-17. <q>A digital representation can have only specific discrete values</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Digital+Design+with+CPLD+Applications+and+VHDL&rft.pub=Thomson%2FDelmar+Learning&rft.date=2005&rft.isbn=1401840302&rft.au=Robert+K.+Dueck&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D1eO7kLWUmYIC%26q%3Ddigital%2520signal%2520logic%26pg%3DPA4&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" 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="CITEREFProakisManolakis2007" class="citation book cs1">Proakis, John G.; <a href="/wiki/Dimitris_Manolakis" title="Dimitris Manolakis">Manolakis, Dimitris G.</a> (2007-01-01). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=H_5SAAAAMAAJ"><i>Digital Signal Processing</i></a>. Pearson Prentice Hall. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780131873742" title="Special:BookSources/9780131873742"><bdi>9780131873742</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160520061336/https://books.google.com/books?id=H_5SAAAAMAAJ">Archived</a> from the original on 2016-05-20.</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.pub=Pearson+Prentice+Hall&rft.date=2007-01-01&rft.isbn=9780131873742&rft.aulast=Proakis&rft.aufirst=John+G.&rft.au=Manolakis%2C+Dimitris+G.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DH_5SAAAAMAAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" class="Z3988"></span></span> </li> <li id="cite_note-waveform-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-waveform_11-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmillie1999" class="citation book cs1">Smillie, Grahame (1999-04-02). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20171217234501/https://books.google.com/books?id=WJ9qkNpScFAC&pg=PA3&dq=%22a+digital+signal+is%22+communication&hl=sv&sa=X&ved=0CFoQ6AEwB2oVChMI-MD09ZjjxwIVBAssCh1wnQu4"><i>Analogue and Digital Communication Techniques</i></a>. Elsevier. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780080527147" title="Special:BookSources/9780080527147"><bdi>9780080527147</bdi></a>. Archived from <a rel="nofollow" class="external text" href="https://books.google.com/books?id=WJ9qkNpScFAC&q=%22a+digital+signal+is%22+communication&pg=PA3">the original</a> on 2017-12-17. <q>A digital signal is a complex waveform and can be defined as a discrete waveform having a finite set of levels</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Analogue+and+Digital+Communication+Techniques&rft.pub=Elsevier&rft.date=1999-04-02&rft.isbn=9780080527147&rft.aulast=Smillie&rft.aufirst=Grahame&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DWJ9qkNpScFAC%26q%3D%2522a%2Bdigital%2Bsignal%2Bis%2522%2Bcommunication%26pg%3DPA3&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.chegg.com/homework-help/definitions/digital-signal-4">"Digital Signal"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190402155546/https://www.chegg.com/homework-help/definitions/digital-signal-4">Archived</a> from the original on 2019-04-02<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-08-13</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Digital+Signal&rft_id=http%3A%2F%2Fwww.chegg.com%2Fhomework-help%2Fdefinitions%2Fdigital-signal-4&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" 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="CITEREFPaul_HorowitzWinfield_Hill2015" class="citation book cs1">Paul Horowitz; Winfield Hill (2015). <i>The Art of Electronics</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780521809269" title="Special:BookSources/9780521809269"><bdi>9780521809269</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+Art+of+Electronics&rft.pub=Cambridge+University+Press&rft.date=2015&rft.isbn=9780521809269&rft.au=Paul+Horowitz&rft.au=Winfield+Hill&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" class="Z3988"></span></span> </li> <li id="cite_note-Khanna-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-Khanna_14-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVinod_Kumar_Khanna2009" class="citation book cs1">Vinod Kumar Khanna (2009). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Vf2qXAbn58oC"><i>Digital Signal Processing</i></a>. S. Chand. p. 3. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9788121930956" title="Special:BookSources/9788121930956"><bdi>9788121930956</bdi></a>. <q>A digital signal is a special form of discrete-time signal which is discrete in both time and amplitude, obtained by permitting each value (sample) of a discrete-time signal to acquire a finite set of values (quantization), assigning it a numerical symbol according to a code ... A digital signal is a sequence or list of numbers drawn from a finite set.</q></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=3&rft.pub=S.+Chand&rft.date=2009&rft.isbn=9788121930956&rft.au=Vinod+Kumar+Khanna&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DVf2qXAbn58oC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" 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="CITEREFSklar2001" class="citation book cs1">Sklar, Bernard (2001). <i>Digital communications : fundamentals and applications</i> (2nd ed.). Upper Saddle River, N.J.: Prentice-Hall PTR. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0130847887" title="Special:BookSources/0130847887"><bdi>0130847887</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/45823120">45823120</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Digital+communications+%3A+fundamentals+and+applications&rft.place=Upper+Saddle+River%2C+N.J.&rft.edition=2nd&rft.pub=Prentice-Hall+PTR&rft.date=2001&rft_id=info%3Aoclcnum%2F45823120&rft.isbn=0130847887&rft.aulast=Sklar&rft.aufirst=Bernard&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZiemerTranter2014" class="citation book cs1">Ziemer, Rodger E.; Tranter, William H. (2014-03-17). <i>Principles of communication : systems, modulation, and noise</i> (Seventh ed.). Hoboken, New Jersey: Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781118078914" title="Special:BookSources/9781118078914"><bdi>9781118078914</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/856647730">856647730</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Principles+of+communication+%3A+systems%2C+modulation%2C+and+noise&rft.place=Hoboken%2C+New+Jersey&rft.edition=Seventh&rft.pub=Wiley&rft.date=2014-03-17&rft_id=info%3Aoclcnum%2F856647730&rft.isbn=9781118078914&rft.aulast=Ziemer&rft.aufirst=Rodger+E.&rft.au=Tranter%2C+William+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" class="Z3988"></span></span> </li> <li id="cite_note-Lu-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-Lu_17-0">^</a></b></span> <span class="reference-text"> For an example from robotics, see <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFK_NishioT_Yasuda2011" class="citation book cs1">K Nishio & T Yasuda (2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=cU4skcyGRFUC&pg=PA506">"Analog–digital circuit for motion detection based on vertebrate retina and its application to mobile robot"</a>. In Bao-Liang Lu; Liqing Zhang & James Kwok (eds.). <i>Neural Information Processing: 18th International Conference, Iconip 2011, Shanghai, China, November 13–17, 2011</i>. Springer. pp. 506 <i>ff</i>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3642249648" title="Special:BookSources/978-3642249648"><bdi>978-3642249648</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130602151534/http://books.google.com/books?id=cU4skcyGRFUC&pg=PA506">Archived</a> from the original on 2013-06-02.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Analog%E2%80%93digital+circuit+for+motion+detection+based+on+vertebrate+retina+and+its+application+to+mobile+robot&rft.btitle=Neural+Information+Processing%3A+18th+International+Conference%2C+Iconip+2011%2C+Shanghai%2C+China%2C+November+13%E2%80%9317%2C+2011&rft.pages=506+%27%27ff%27%27&rft.pub=Springer&rft.date=2011&rft.isbn=978-3642249648&rft.au=K+Nishio&rft.au=T+Yasuda&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DcU4skcyGRFUC%26pg%3DPA506&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" class="Z3988"></span></span> </li> <li id="cite_note-gyro-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-gyro_18-0">^</a></b></span> <span class="reference-text"> For example, see <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFM._N._ArmeniseCaterina_CiminelliFrancesco_Dell'OlioVittorio_Passaro2010" class="citation book cs1">M. N. Armenise; Caterina Ciminelli; Francesco Dell'Olio; Vittorio Passaro (2010). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=lJUiyigJRBgC&pg=PA47">"§4.3 Optical gyros based on a fiber ring laser"</a>. <i>Advances in Gyroscope Technologies</i>. Springer. p. 47. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3642154935" title="Special:BookSources/978-3642154935"><bdi>978-3642154935</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130602165007/http://books.google.com/books?id=lJUiyigJRBgC&pg=PA47">Archived</a> from the original on 2013-06-02.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=%C2%A74.3+Optical+gyros+based+on+a+fiber+ring+laser&rft.btitle=Advances+in+Gyroscope+Technologies&rft.pages=47&rft.pub=Springer&rft.date=2010&rft.isbn=978-3642154935&rft.au=M.+N.+Armenise&rft.au=Caterina+Ciminelli&rft.au=Francesco+Dell%27Olio&rft.au=Vittorio+Passaro&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DlJUiyigJRBgC%26pg%3DPA47&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" class="Z3988"></span></span> </li> <li id="cite_note-Chambers-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-Chambers_19-0">^</a></b></span> <span class="reference-text"> The optical reading process is described by <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMark_L._Chambers2004" class="citation book cs1">Mark L. Chambers (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=VKsAroUnIxsC&pg=PA13"><i>CD & DVD Recording for Dummies</i></a> (2nd ed.). John Wiley & Sons. p. 13. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0764559563" title="Special:BookSources/978-0764559563"><bdi>978-0764559563</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130602154240/http://books.google.com/books?id=VKsAroUnIxsC&pg=PA13">Archived</a> from the original on 2013-06-02.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=CD+%26+DVD+Recording+for+Dummies&rft.pages=13&rft.edition=2nd&rft.pub=John+Wiley+%26+Sons&rft.date=2004&rft.isbn=978-0764559563&rft.au=Mark+L.+Chambers&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DVKsAroUnIxsC%26pg%3DPA13&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" class="Z3988"></span></span> </li> <li id="cite_note-McMahon_s_and_s-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-McMahon_s_and_s_20-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavid_McMahon2007" class="citation book cs1">David McMahon (2007). <a rel="nofollow" class="external text" href="https://www.amazon.com/gp/product/0071475788?selectObb=new"><i>Signals & Systems Demystified</i></a>. New York: McGraw Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-147578-5" title="Special:BookSources/978-0-07-147578-5"><bdi>978-0-07-147578-5</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200122152613/https://www.amazon.com/gp/product/0071475788?selectObb=new">Archived</a> from the original on 2020-01-22<span class="reference-accessdate">. Retrieved <span class="nowrap">2017-09-11</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Signals+%26+Systems+Demystified&rft.place=New+York&rft.pub=McGraw+Hill&rft.date=2007&rft.isbn=978-0-07-147578-5&rft.au=David+McMahon&rft_id=https%3A%2F%2Fwww.amazon.com%2Fgp%2Fproduct%2F0071475788%3FselectObb%3Dnew&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" class="Z3988"></span></span> </li> <li id="cite_note-Signals_and_systems-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-Signals_and_systems_21-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFM.J._Roberts2011" class="citation book cs1">M.J. Roberts (2011). <i>Signals and Systems: Analysis Using Transform Methods & MATLAB</i>. New York: McGraw Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0073380681" title="Special:BookSources/978-0073380681"><bdi>978-0073380681</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Signals+and+Systems%3A+Analysis+Using+Transform+Methods+%26+MATLAB&rft.place=New+York&rft.pub=McGraw+Hill&rft.date=2011&rft.isbn=978-0073380681&rft.au=M.J.+Roberts&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" 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&action=edit&section=19" 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="CITEREFHsu,_P._H.1995" class="citation book cs1">Hsu, P. H. (1995). <i>Schaum's Theory and Problems: Signals and Systems</i>. McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-07-030641-9" title="Special:BookSources/0-07-030641-9"><bdi>0-07-030641-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Schaum%27s+Theory+and+Problems%3A+Signals+and+Systems&rft.pub=McGraw-Hill&rft.date=1995&rft.isbn=0-07-030641-9&rft.au=Hsu%2C+P.+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLathi,_B.P.1998" class="citation book cs1">Lathi, B.P. (1998). <i>Signal Processing & Linear Systems</i>. Berkeley-Cambridge Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-941413-35-7" title="Special:BookSources/0-941413-35-7"><bdi>0-941413-35-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Signal+Processing+%26+Linear+Systems&rft.pub=Berkeley-Cambridge+Press&rft.date=1998&rft.isbn=0-941413-35-7&rft.au=Lathi%2C+B.P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal" class="Z3988"></span></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 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