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</ul> </li> </ul> </li> <li id="toc-Alternative_definition" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Alternative_definition"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Alternative definition</span> </div> </a> <ul id="toc-Alternative_definition-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Modulation_system_measurements" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Modulation_system_measurements"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Modulation system measurements</span> </div> </a> <button aria-controls="toc-Modulation_system_measurements-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 Modulation system measurements subsection</span> </button> <ul id="toc-Modulation_system_measurements-sublist" class="vector-toc-list"> <li id="toc-Amplitude_modulation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Amplitude_modulation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Amplitude modulation</span> </div> </a> <ul id="toc-Amplitude_modulation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Frequency_modulation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Frequency_modulation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Frequency modulation</span> </div> </a> <ul id="toc-Frequency_modulation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Noise_reduction" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Noise_reduction"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Noise reduction</span> </div> </a> <ul id="toc-Noise_reduction-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Digital_signals" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Digital_signals"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Digital signals</span> </div> </a> <button aria-controls="toc-Digital_signals-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 Digital signals subsection</span> </button> <ul id="toc-Digital_signals-sublist" class="vector-toc-list"> <li id="toc-Fixed_point" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fixed_point"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Fixed point</span> </div> </a> <ul id="toc-Fixed_point-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Floating_point" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Floating_point"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Floating point</span> </div> </a> <ul id="toc-Floating_point-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Optical_signals" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Optical_signals"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Optical signals</span> </div> </a> <ul id="toc-Optical_signals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Types_and_abbreviations" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Types_and_abbreviations"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Types and abbreviations</span> </div> </a> <ul id="toc-Types_and_abbreviations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other_uses" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Other_uses"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Other uses</span> </div> </a> <ul id="toc-Other_uses-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Similar_concepts" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Similar_concepts"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Similar concepts</span> </div> </a> <ul id="toc-Similar_concepts-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">10</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">11</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">12</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">13</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Signal-to-noise ratio</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 35 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-35" 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">35 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B3%D8%A8%D8%A9_%D8%A7%D9%84%D8%A5%D8%B4%D8%A7%D8%B1%D8%A9_%D8%A5%D9%84%D9%89_%D8%A7%D9%84%D8%B6%D8%AC%D9%8A%D8%AC" title="نسبة الإشارة إلى الضجيج – Arabic" lang="ar" hreflang="ar" data-title="نسبة الإشارة إلى الضجيج" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</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%85%E0%A6%AA%E0%A6%B8%E0%A6%82%E0%A6%95%E0%A7%87%E0%A6%A4_%E0%A6%85%E0%A6%A8%E0%A7%81%E0%A6%AA%E0%A6%BE%E0%A6%A4" title="সংকেত-অপসংকেত অনুপাত – Bangla" lang="bn" hreflang="bn" data-title="সংকেত-অপসংকেত অনুপাত" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9E%D1%82%D0%BD%D0%BE%D1%88%D0%B5%D0%BD%D0%B8%D0%B5_%D1%81%D0%B8%D0%B3%D0%BD%D0%B0%D0%BB-%D0%BA%D1%8A%D0%BC-%D1%88%D1%83%D0%BC" title="Отношение сигнал-към-шум – Bulgarian" lang="bg" hreflang="bg" data-title="Отношение сигнал-към-шум" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Relaci%C3%B3_senyal-soroll" title="Relació senyal-soroll – Catalan" lang="ca" hreflang="ca" data-title="Relació senyal-soroll" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Pom%C4%9Br_sign%C3%A1lu_a_%C5%A1umu" title="Poměr signálu a šumu – Czech" lang="cs" hreflang="cs" data-title="Poměr signálu a šumu" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Signal-Rausch-Verh%C3%A4ltnis" title="Signal-Rausch-Verhältnis – German" lang="de" hreflang="de" data-title="Signal-Rausch-Verhältnis" 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/Signaali-m%C3%BCra_suhe" title="Signaali-müra suhe – Estonian" lang="et" hreflang="et" data-title="Signaali-müra suhe" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Relaci%C3%B3n_se%C3%B1al/ruido" title="Relación señal/ruido – Spanish" lang="es" hreflang="es" data-title="Relación señal/ruido" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Seinale/zarata_ratio" title="Seinale/zarata ratio – Basque" lang="eu" hreflang="eu" data-title="Seinale/zarata ratio" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%86%D8%B3%D8%A8%D8%AA_%D8%B3%DB%8C%DA%AF%D9%86%D8%A7%D9%84_%D8%A8%D9%87_%D9%86%D9%88%DB%8C%D8%B2" title="نسبت سیگنال به نویز – Persian" lang="fa" hreflang="fa" data-title="نسبت سیگنال به نویز" 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/Rapport_signal_sur_bruit" title="Rapport signal sur bruit – French" lang="fr" hreflang="fr" data-title="Rapport signal sur bruit" 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/Relaci%C3%B3n_sinal/ru%C3%ADdo" title="Relación sinal/ruído – Galician" lang="gl" hreflang="gl" data-title="Relación sinal/ruído" 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_%EB%8C%80_%EC%9E%A1%EC%9D%8C%EB%B9%84" title="신호 대 잡음비 – Korean" lang="ko" hreflang="ko" data-title="신호 대 잡음비" 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%BF%E0%A4%97%E0%A4%A8%E0%A4%B2-%E0%A4%B0%E0%A4%B5_%E0%A4%85%E0%A4%A8%E0%A5%81%E0%A4%AA%E0%A4%BE%E0%A4%A4" title="सिगनल-रव अनुपात – Hindi" lang="hi" hreflang="hi" data-title="सिगनल-रव अनुपात" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Nisbah_sinyal%E2%80%93derau" title="Nisbah sinyal–derau – Indonesian" lang="id" hreflang="id" data-title="Nisbah sinyal–derau" 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/Rapporto_segnale/rumore" title="Rapporto segnale/rumore – Italian" lang="it" hreflang="it" data-title="Rapporto segnale/rumore" 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%99%D7%97%D7%A1_%D7%90%D7%95%D7%AA_%D7%9C%D7%A8%D7%A2%D7%A9" title="יחס אות לרעש – Hebrew" lang="he" hreflang="he" data-title="יחס אות לרעש" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Signalo_ir_triuk%C5%A1mo_santykis" title="Signalo ir triukšmo santykis – Lithuanian" lang="lt" hreflang="lt" data-title="Signalo ir triukšmo santykis" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Jel-zaj_viszony" title="Jel-zaj viszony – Hungarian" lang="hu" hreflang="hu" data-title="Jel-zaj viszony" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Signaal-ruisverhouding" title="Signaal-ruisverhouding – Dutch" lang="nl" hreflang="nl" data-title="Signaal-ruisverhouding" 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/SN%E6%AF%94" title="SN比 – Japanese" lang="ja" hreflang="ja" data-title="SN比" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Signal-st%C3%B8y-forhold" title="Signal-støy-forhold – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Signal-støy-forhold" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Signal-til-st%C3%B8y-tilh%C3%B8ve" title="Signal-til-støy-tilhøve – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Signal-til-støy-tilhøve" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Stosunek_sygna%C5%82u_do_szumu" title="Stosunek sygnału do szumu – Polish" lang="pl" hreflang="pl" data-title="Stosunek sygnału do szumu" 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/Rela%C3%A7%C3%A3o_sinal-ru%C3%ADdo" title="Relação sinal-ruído – Portuguese" lang="pt" hreflang="pt" data-title="Relação sinal-ruído" 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/Raport_semnal/zgomot" title="Raport semnal/zgomot – Romanian" lang="ro" hreflang="ro" data-title="Raport semnal/zgomot" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9E%D1%82%D0%BD%D0%BE%D1%88%D0%B5%D0%BD%D0%B8%D0%B5_%D1%81%D0%B8%D0%B3%D0%BD%D0%B0%D0%BB/%D1%88%D1%83%D0%BC" title="Отношение сигнал/шум – Russian" lang="ru" hreflang="ru" data-title="Отношение сигнал/шум" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Signaali-kohinasuhde" title="Signaali-kohinasuhde – Finnish" lang="fi" hreflang="fi" data-title="Signaali-kohinasuhde" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Signal-brusf%C3%B6rh%C3%A5llande" title="Signal-brusförhållande – Swedish" lang="sv" hreflang="sv" data-title="Signal-brusförhållande" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AD%E0%B8%B1%E0%B8%95%E0%B8%A3%E0%B8%B2%E0%B8%AA%E0%B9%88%E0%B8%A7%E0%B8%99%E0%B8%AA%E0%B8%B1%E0%B8%8D%E0%B8%8D%E0%B8%B2%E0%B8%93%E0%B8%95%E0%B9%88%E0%B8%AD%E0%B8%AA%E0%B8%B1%E0%B8%8D%E0%B8%8D%E0%B8%B2%E0%B8%93%E0%B8%A3%E0%B8%9A%E0%B8%81%E0%B8%A7%E0%B8%99" title="อัตราส่วนสัญญาณต่อสัญญาณรบกวน – Thai" lang="th" hreflang="th" data-title="อัตราส่วนสัญญาณต่อสัญญาณรบกวน" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Sinyal_G%C3%BCr%C3%BClt%C3%BC_Oran%C4%B1" title="Sinyal Gürültü Oranı – Turkish" lang="tr" hreflang="tr" data-title="Sinyal Gürültü Oranı" 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 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.hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Signal-to-noise" redirects here. For statistics, see <a href="/wiki/Effect_size" title="Effect size">Effect size</a>. For other uses, see <a href="/wiki/Signal-to-noise_(disambiguation)" class="mw-redirect mw-disambig" title="Signal-to-noise (disambiguation)">Signal-to-noise (disambiguation)</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="/wiki/Signal-to-interference-plus-noise_ratio" title="Signal-to-interference-plus-noise ratio">Signal-to-interference-plus-noise ratio</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:SNR_image_demonstration.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/SNR_image_demonstration.png/220px-SNR_image_demonstration.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/SNR_image_demonstration.png/330px-SNR_image_demonstration.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f9/SNR_image_demonstration.png/440px-SNR_image_demonstration.png 2x" data-file-width="3840" data-file-height="2880" /></a><figcaption>A gray-scale photography with different signal-to-noise ratios (SNRs). The SNR values are given for the rectangular region on the forehead. The plots at the bottom show the signal intensity in the indicated row of the image (red: original signal, blue: with noise).</figcaption></figure> <p><b>Signal-to-noise ratio</b> (<b>SNR</b> or <b>S/N</b>) is a measure used in <a href="/wiki/Science_and_engineering" class="mw-redirect" title="Science and engineering">science and engineering</a> that compares the level of a desired <a href="/wiki/Signal" title="Signal">signal</a> to the level of background <a href="/wiki/Noise_(signal_processing)" title="Noise (signal processing)">noise</a>. SNR is defined as the ratio of signal <a href="/wiki/Power_(physics)" title="Power (physics)">power</a> to <a href="/wiki/Noise_power" title="Noise power">noise power</a>, often expressed in <a href="/wiki/Decibel" title="Decibel">decibels</a>. A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise. </p><p>SNR is an important parameter that affects the performance and quality of systems that process or transmit signals, such as <a href="/wiki/Communication_system" class="mw-redirect" title="Communication system">communication systems</a>, <a href="/wiki/Audio_system" class="mw-redirect" title="Audio system">audio systems</a>, <a href="/wiki/Radar_system" class="mw-redirect" title="Radar system">radar systems</a>, <a href="/wiki/Imaging_system" class="mw-redirect" title="Imaging system">imaging systems</a>, and <a href="/wiki/Data_acquisition" title="Data acquisition">data acquisition</a> systems. A high SNR means that the signal is clear and easy to detect or interpret, while a low SNR means that the signal is corrupted or obscured by noise and may be difficult to distinguish or recover. SNR can be improved by various methods, such as increasing the signal strength, reducing the noise level, filtering out unwanted noise, or using error correction techniques. </p><p>SNR also determines the maximum possible amount of data that can be transmitted reliably over a given channel, which depends on its bandwidth and SNR. This relationship is described by the <a href="/wiki/Shannon%E2%80%93Hartley_theorem" title="Shannon–Hartley theorem">Shannon–Hartley theorem</a>, which is a fundamental law of information theory. </p><p>SNR can be calculated using different formulas depending on how the signal and noise are measured and defined. The most common way to express SNR is in decibels, which is a logarithmic scale that makes it easier to compare large or small values. Other definitions of SNR may use different factors or bases for the logarithm, depending on the context and application. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definition">Definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal-to-noise_ratio&action=edit&section=1" title="Edit section: Definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Unreferenced_section plainlinks metadata ambox ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Signal-to-noise_ratio" title="Special:EditPage/Signal-to-noise ratio">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">February 2022</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>One definition of signal-to-noise ratio is the ratio of the <a href="/wiki/Power_(physics)" title="Power (physics)">power</a> of a <a href="/wiki/Signal" title="Signal">signal</a> (meaningful input) to the power of background <a href="/wiki/Noise_(electronic)" class="mw-redirect" title="Noise (electronic)">noise</a> (meaningless or unwanted input): </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 \mathrm {SNR} ={\frac {P_{\mathrm {signal} }}{P_{\mathrm {noise} }}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">R</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> </mrow> </mrow> </msub> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {SNR} ={\frac {P_{\mathrm {signal} }}{P_{\mathrm {noise} }}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08b8624b51933d2f1f11233693840cd5139e42c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:15.173ex; height:6.009ex;" alt="{\displaystyle \mathrm {SNR} ={\frac {P_{\mathrm {signal} }}{P_{\mathrm {noise} }}},}"></span></dd></dl> <p>where <span class="texhtml mvar" style="font-style:italic;">P</span> is average power. Both signal and noise power must be measured at the same or equivalent points in a system, and within the same system <a href="/wiki/Bandwidth_(signal_processing)" title="Bandwidth (signal processing)">bandwidth</a>. </p><p>The signal-to-noise ratio of a random variable (<span class="texhtml mvar" style="font-style:italic;">S</span>) to random noise <span class="texhtml mvar" style="font-style:italic;">N</span> is:<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {SNR} ={\frac {\mathrm {E} [S^{2}]}{\mathrm {E} [N^{2}]}}\,,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">R</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> <mo stretchy="false">[</mo> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> <mo stretchy="false">[</mo> <msup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {SNR} ={\frac {\mathrm {E} [S^{2}]}{\mathrm {E} [N^{2}]}}\,,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/604c064886a33db6d1f75a52b30adafe2da8108e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:15.768ex; height:6.676ex;" alt="{\displaystyle \mathrm {SNR} ={\frac {\mathrm {E} [S^{2}]}{\mathrm {E} [N^{2}]}}\,,}"></span> </p><p>where E refers to the <a href="/wiki/Expected_value" title="Expected value">expected value</a>, which in this case is the <a href="/wiki/Mean_square" title="Mean square">mean square</a> of <span class="texhtml mvar" style="font-style:italic;">N</span>. </p><p>If the signal is simply a constant value of <i><span class="texhtml mvar" style="font-style:italic;">s</span></i>, this equation simplifies to: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {SNR} ={\frac {s^{2}}{\mathrm {E} [N^{2}]}}\,.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">R</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> <mo stretchy="false">[</mo> <msup> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {SNR} ={\frac {s^{2}}{\mathrm {E} [N^{2}]}}\,.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4984650250cb4e6b60cce683fab4e171fb8541fe" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:15.768ex; height:6.509ex;" alt="{\displaystyle \mathrm {SNR} ={\frac {s^{2}}{\mathrm {E} [N^{2}]}}\,.}"></span> </p><p>If the noise has <a href="/wiki/Expected_value" title="Expected value">expected value</a> of zero, as is common, the denominator is its <a href="/wiki/Variance" title="Variance">variance</a>, the square of its <a href="/wiki/Standard_deviation" title="Standard deviation">standard deviation</a> <span class="texhtml"><i>σ</i><sub>N</sub></span>. </p><p>The signal and the noise must be measured the same way, for example as voltages across the same <a href="/wiki/Electrical_impedance" title="Electrical impedance">impedance</a>. Their <a href="/wiki/Root_mean_square" title="Root mean square">root mean squares</a> can alternatively be used according to: </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 \mathrm {SNR} ={\frac {P_{\mathrm {signal} }}{P_{\mathrm {noise} }}}=\left({\frac {A_{\mathrm {signal} }}{A_{\mathrm {noise} }}}\right)^{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">R</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> </mrow> </mrow> </msub> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> </mrow> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {SNR} ={\frac {P_{\mathrm {signal} }}{P_{\mathrm {noise} }}}=\left({\frac {A_{\mathrm {signal} }}{A_{\mathrm {noise} }}}\right)^{2},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/461bfca476e25f7981fef5503cc0baa69365f193" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:29.679ex; height:6.843ex;" alt="{\displaystyle \mathrm {SNR} ={\frac {P_{\mathrm {signal} }}{P_{\mathrm {noise} }}}=\left({\frac {A_{\mathrm {signal} }}{A_{\mathrm {noise} }}}\right)^{2},}"></span></dd></dl> <p>where <span class="texhtml mvar" style="font-style:italic;">A</span> is <a href="/wiki/Root_mean_square_(RMS)_amplitude" class="mw-redirect" title="Root mean square (RMS) amplitude">root mean square (RMS) amplitude</a> (for example, RMS voltage). </p> <div class="mw-heading mw-heading3"><h3 id="Decibels">Decibels</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal-to-noise_ratio&action=edit&section=2" title="Edit section: Decibels"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Because many signals have a very wide <a href="/wiki/Dynamic_range" title="Dynamic range">dynamic range</a>, signals are often expressed using the <a href="/wiki/Logarithm" title="Logarithm">logarithmic</a> <a href="/wiki/Decibel" title="Decibel">decibel</a> scale. Based upon the definition of decibel, signal and noise may be expressed in decibels (dB) as </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 P_{\mathrm {signal,dB} }=10\log _{10}\left(P_{\mathrm {signal} }\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> <mo>,</mo> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>=</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> </mrow> </mrow> </msub> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\mathrm {signal,dB} }=10\log _{10}\left(P_{\mathrm {signal} }\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ede8481905eb1e80910590949e9b50de14b6358" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:26.693ex; height:3.009ex;" alt="{\displaystyle P_{\mathrm {signal,dB} }=10\log _{10}\left(P_{\mathrm {signal} }\right)}"></span></dd></dl> <p>and </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 P_{\mathrm {noise,dB} }=10\log _{10}\left(P_{\mathrm {noise} }\right).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">e</mi> <mo>,</mo> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>=</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo>)</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{\mathrm {noise,dB} }=10\log _{10}\left(P_{\mathrm {noise} }\right).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5eca62639a1852727f2d235e1b1e035268261ca9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:26.241ex; height:3.009ex;" alt="{\displaystyle P_{\mathrm {noise,dB} }=10\log _{10}\left(P_{\mathrm {noise} }\right).}"></span></dd></dl> <p>In a similar manner, SNR may be expressed in decibels as </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 \mathrm {SNR_{dB}} =10\log _{10}\left(\mathrm {SNR} \right).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">N</mi> <msub> <mi mathvariant="normal">R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> </msub> </mrow> <mo>=</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">R</mi> </mrow> <mo>)</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {SNR_{dB}} =10\log _{10}\left(\mathrm {SNR} \right).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f0c32ab616a20aef16224c05685f7f32bb10736" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.917ex; height:2.843ex;" alt="{\displaystyle \mathrm {SNR_{dB}} =10\log _{10}\left(\mathrm {SNR} \right).}"></span></dd></dl> <p>Using the definition of SNR </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 \mathrm {SNR_{dB}} =10\log _{10}\left({\frac {P_{\mathrm {signal} }}{P_{\mathrm {noise} }}}\right).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">N</mi> <msub> <mi mathvariant="normal">R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> </msub> </mrow> <mo>=</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> </mrow> </mrow> </msub> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {SNR_{dB}} =10\log _{10}\left({\frac {P_{\mathrm {signal} }}{P_{\mathrm {noise} }}}\right).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a7b11f600ce6e7defb4f20ffa8071818b6baa14" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:28.464ex; height:6.176ex;" alt="{\displaystyle \mathrm {SNR_{dB}} =10\log _{10}\left({\frac {P_{\mathrm {signal} }}{P_{\mathrm {noise} }}}\right).}"></span></dd></dl> <p>Using the quotient rule for logarithms </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 10\log _{10}\left({\frac {P_{\mathrm {signal} }}{P_{\mathrm {noise} }}}\right)=10\log _{10}\left(P_{\mathrm {signal} }\right)-10\log _{10}\left(P_{\mathrm {noise} }\right).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> </mrow> </mrow> </msub> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> </mrow> </mrow> </msub> <mo>)</mo> </mrow> <mo>−</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> <mo>)</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10\log _{10}\left({\frac {P_{\mathrm {signal} }}{P_{\mathrm {noise} }}}\right)=10\log _{10}\left(P_{\mathrm {signal} }\right)-10\log _{10}\left(P_{\mathrm {noise} }\right).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8a0963feb78d1968699c1f9852f1b7dd60ccd7c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:54.127ex; height:6.176ex;" alt="{\displaystyle 10\log _{10}\left({\frac {P_{\mathrm {signal} }}{P_{\mathrm {noise} }}}\right)=10\log _{10}\left(P_{\mathrm {signal} }\right)-10\log _{10}\left(P_{\mathrm {noise} }\right).}"></span></dd></dl> <p>Substituting the definitions of SNR, signal, and noise in decibels into the above equation results in an important formula for calculating the signal to noise ratio in decibels, when the signal and noise are also in decibels: </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 \mathrm {SNR_{dB}} ={P_{\mathrm {signal,dB} }-P_{\mathrm {noise,dB} }}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">N</mi> <msub> <mi mathvariant="normal">R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> <mo>,</mo> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">e</mi> <mo>,</mo> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {SNR_{dB}} ={P_{\mathrm {signal,dB} }-P_{\mathrm {noise,dB} }}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/941dbd0dd4bed8612c3eec1cedf4aa16805f02ce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:29.852ex; height:2.843ex;" alt="{\displaystyle \mathrm {SNR_{dB}} ={P_{\mathrm {signal,dB} }-P_{\mathrm {noise,dB} }}.}"></span></dd></dl> <p>In the above formula, P is measured in units of power, such as watts (W) or milliwatts (mW), and the signal-to-noise ratio is a pure number. </p><p>However, when the signal and noise are measured in volts (V) or amperes (A), which are measures of amplitude,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>note 1<span class="cite-bracket">]</span></a></sup> they must first be squared to obtain a quantity proportional to power, as shown below: </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 \mathrm {SNR_{dB}} =10\log _{10}\left[\left({\frac {A_{\mathrm {signal} }}{A_{\mathrm {noise} }}}\right)^{2}\right]=20\log _{10}\left({\frac {A_{\mathrm {signal} }}{A_{\mathrm {noise} }}}\right)={A_{\mathrm {signal,dB} }-A_{\mathrm {noise,dB} }}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">N</mi> <msub> <mi mathvariant="normal">R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> </msub> </mrow> <mo>=</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>[</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> </mrow> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>]</mo> </mrow> <mo>=</mo> <mn>20</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> </mrow> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">e</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> <mo>,</mo> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <mo>−</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">e</mi> <mo>,</mo> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {SNR_{dB}} =10\log _{10}\left[\left({\frac {A_{\mathrm {signal} }}{A_{\mathrm {noise} }}}\right)^{2}\right]=20\log _{10}\left({\frac {A_{\mathrm {signal} }}{A_{\mathrm {noise} }}}\right)={A_{\mathrm {signal,dB} }-A_{\mathrm {noise,dB} }}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a5a7ee342aeb7abd78f5bd9914fe234cd0eedf5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:76.142ex; height:7.509ex;" alt="{\displaystyle \mathrm {SNR_{dB}} =10\log _{10}\left[\left({\frac {A_{\mathrm {signal} }}{A_{\mathrm {noise} }}}\right)^{2}\right]=20\log _{10}\left({\frac {A_{\mathrm {signal} }}{A_{\mathrm {noise} }}}\right)={A_{\mathrm {signal,dB} }-A_{\mathrm {noise,dB} }}.}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Dynamic_range">Dynamic range</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal-to-noise_ratio&action=edit&section=3" title="Edit section: Dynamic range"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The concepts of signal-to-noise ratio<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> and dynamic range are closely related. Dynamic range measures the ratio between the strongest un-<a href="/wiki/Distortion" title="Distortion">distorted</a> signal on a <a href="/wiki/Communication_channel" title="Communication channel">channel</a> and the minimum discernible signal, which for most purposes is the noise level. SNR measures the ratio between an arbitrary signal level (not necessarily the most powerful signal possible) and noise. Measuring signal-to-noise ratios requires the selection of a representative or <i>reference</i> signal. In <a href="/wiki/Audio_engineering" class="mw-redirect" title="Audio engineering">audio engineering</a>, the reference signal is usually a <a href="/wiki/Sine_wave" title="Sine wave">sine wave</a> at a standardized <a href="/wiki/Nominal_level" title="Nominal level">nominal</a> or <a href="/wiki/Alignment_level" title="Alignment level">alignment level</a>, such as 1 kHz at +4 <a href="/wiki/DBu" class="mw-redirect" title="DBu">dBu</a> (1.228 V<sub>RMS</sub>). </p><p>SNR is usually taken to indicate an <i>average</i> signal-to-noise ratio, as it is possible that instantaneous signal-to-noise ratios will be considerably different. The concept can be understood as normalizing the noise level to 1 (0 dB) and measuring how far the signal 'stands out'. </p> <div class="mw-heading mw-heading3"><h3 id="Difference_from_conventional_power">Difference from conventional power</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal-to-noise_ratio&action=edit&section=4" title="Edit section: Difference from conventional power"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In physics, the average <a href="/wiki/Power_(physics)" title="Power (physics)">power</a> of an AC signal is defined as the average value of voltage times current; for <a href="/wiki/Resistive" class="mw-redirect" title="Resistive">resistive</a> (non-<a href="/wiki/Reactance_(electronics)" class="mw-redirect" title="Reactance (electronics)">reactive</a>) circuits, where voltage and current are in phase, this is equivalent to the product of the <a href="/wiki/Root_mean_square" title="Root mean square">rms</a> voltage and current: </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 \mathrm {P} =V_{\mathrm {rms} }I_{\mathrm {rms} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> <mo>=</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {P} =V_{\mathrm {rms} }I_{\mathrm {rms} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45c69055e761c61c2c6ddd76099a87ac8e5025ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.847ex; height:2.509ex;" alt="{\displaystyle \mathrm {P} =V_{\mathrm {rms} }I_{\mathrm {rms} }}"></span></dd></dl> <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 \mathrm {P} ={\frac {V_{\mathrm {rms} }^{2}}{R}}=I_{\mathrm {rms} }^{2}R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mi>R</mi> </mfrac> </mrow> <mo>=</mo> <msubsup> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {P} ={\frac {V_{\mathrm {rms} }^{2}}{R}}=I_{\mathrm {rms} }^{2}R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103303e09b8624560f90b3b45027d6954d7a357f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:18.546ex; height:5.676ex;" alt="{\displaystyle \mathrm {P} ={\frac {V_{\mathrm {rms} }^{2}}{R}}=I_{\mathrm {rms} }^{2}R}"></span></dd></dl> <p>But in signal processing and communication, one usually assumes that <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 R=1\Omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <mn>1</mn> <mi mathvariant="normal">Ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R=1\Omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5cd5cdbf4d2ac37feb13e40ea9feb8e88607db21" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.703ex; height:2.176ex;" alt="{\displaystyle R=1\Omega }"></span> <sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> so that factor is usually not included while measuring power or energy of a signal. This may cause some confusion among readers, but the resistance factor is not significant for typical operations performed in signal processing, or for computing power ratios. For most cases, the power of a signal would be considered to be simply </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 \mathrm {P} =V_{\mathrm {rms} }^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">P</mi> </mrow> <mo>=</mo> <msubsup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {P} =V_{\mathrm {rms} }^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db157679a528775041b7f5b38cacea6247d4545f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.93ex; height:2.843ex;" alt="{\displaystyle \mathrm {P} =V_{\mathrm {rms} }^{2}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Alternative_definition">Alternative definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal-to-noise_ratio&action=edit&section=5" title="Edit section: Alternative definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An alternative definition of SNR is as the reciprocal of the <a href="/wiki/Coefficient_of_variation" title="Coefficient of variation">coefficient of variation</a>, i.e., the ratio of <a href="/wiki/Mean" title="Mean">mean</a> to <a href="/wiki/Standard_deviation" title="Standard deviation">standard deviation</a> of a signal or measurement:<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-b1_7-0" class="reference"><a href="#cite_note-b1-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </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 \mathrm {SNR} ={\frac {\mu }{\sigma }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">R</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>μ</mi> <mi>σ</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {SNR} ={\frac {\mu }{\sigma }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5078cb5ec4cec9652457504841d315733e39cee4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.082ex; height:4.843ex;" alt="{\displaystyle \mathrm {SNR} ={\frac {\mu }{\sigma }}}"></span></dd></dl> <p>where <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 \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span> is the signal mean or <a href="/wiki/Expected_value" title="Expected value">expected value</a> 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 \sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" 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 \sigma }"></span> is the standard deviation of the noise, or an estimate thereof.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>note 2<span class="cite-bracket">]</span></a></sup> Notice that such an alternative definition is only useful for variables that are always non-negative (such as photon counts and <a href="/wiki/Luminance" title="Luminance">luminance</a>), and it is only an approximation since <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 \operatorname {E} \left[X^{2}\right]=\sigma ^{2}+\mu ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">E</mi> <mo>⁡</mo> <mrow> <mo>[</mo> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>]</mo> </mrow> <mo>=</mo> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {E} \left[X^{2}\right]=\sigma ^{2}+\mu ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fde6832093dc5d9bf035b5c5adea64b33b8f3a37" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:17.353ex; height:3.343ex;" alt="{\displaystyle \operatorname {E} \left[X^{2}\right]=\sigma ^{2}+\mu ^{2}}"></span>. It is commonly used in <a href="/wiki/Image_processing" class="mw-redirect" title="Image processing">image processing</a>,<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> where the SNR of an <a href="/wiki/Image" title="Image">image</a> is usually calculated as the ratio of the <a href="/wiki/Mean" title="Mean">mean</a> pixel value to the <a href="/wiki/Standard_deviation" title="Standard deviation">standard deviation</a> of the pixel values over a given neighborhood. </p><p>Sometimes<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag needs further explanation. (March 2021)">further explanation needed</span></a></i>]</sup> SNR is defined as the square of the alternative definition above, in which case it is equivalent to the <a href="#Definition">more common definition</a>: </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 \mathrm {SNR} ={\frac {\mu ^{2}}{\sigma ^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">R</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>μ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {SNR} ={\frac {\mu ^{2}}{\sigma ^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18f119d31748056cc297455d4eb504de9011b7ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:11.137ex; height:6.009ex;" alt="{\displaystyle \mathrm {SNR} ={\frac {\mu ^{2}}{\sigma ^{2}}}}"></span></dd></dl> <p>This definition is closely related to the <a href="/wiki/Sensitivity_index" title="Sensitivity index">sensitivity index</a> or <i>d<span class="nowrap" style="padding-left:0.1em;">'</span></i>, when assuming that the signal has two states separated by signal amplitude <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 \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span>, and the noise standard deviation <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 \sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" 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 \sigma }"></span> does not change between the two states. </p><p>The <i>Rose criterion</i> (named after <a href="/wiki/Albert_Rose_(physicist)" title="Albert Rose (physicist)">Albert Rose</a>) states that an SNR of at least 5 is needed to be able to distinguish image features with certainty. An SNR less than 5 means less than 100% certainty in identifying image details.<sup id="cite_ref-b1_7-1" class="reference"><a href="#cite_note-b1-7"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>Yet another alternative, very specific, and distinct definition of SNR is employed to characterize <a href="/wiki/Film_speed" title="Film speed">sensitivity</a> of imaging systems; see <a href="/wiki/Signal-to-noise_ratio_(imaging)" title="Signal-to-noise ratio (imaging)">Signal-to-noise ratio (imaging)</a>. </p><p>Related measures are the "<a href="/wiki/Contrast_ratio" title="Contrast ratio">contrast ratio</a>" and the "<a href="/wiki/Contrast-to-noise_ratio" title="Contrast-to-noise ratio">contrast-to-noise ratio</a>". </p> <div class="mw-heading mw-heading2"><h2 id="Modulation_system_measurements">Modulation system measurements</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal-to-noise_ratio&action=edit&section=6" title="Edit section: Modulation system measurements"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Amplitude_modulation">Amplitude modulation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal-to-noise_ratio&action=edit&section=7" title="Edit section: Amplitude modulation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Channel signal-to-noise ratio is given by </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 \mathrm {(SNR)_{C,AM}} ={\frac {A_{C}^{2}(1+k_{a}^{2}P)}{2WN_{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">R</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mo>,</mo> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">M</mi> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <msubsup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mi>P</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mn>2</mn> <mi>W</mi> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {(SNR)_{C,AM}} ={\frac {A_{C}^{2}(1+k_{a}^{2}P)}{2WN_{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65e293a0429c4ec8032c8620b8b5cb660f5658a4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:28.201ex; height:6.509ex;" alt="{\displaystyle \mathrm {(SNR)_{C,AM}} ={\frac {A_{C}^{2}(1+k_{a}^{2}P)}{2WN_{0}}}}"></span></dd></dl> <p>where W is the bandwidth 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 k_{a}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{a}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f18ff97c1cc190c750a7190539c292b4c18e2d89" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.313ex; height:2.509ex;" alt="{\displaystyle k_{a}}"></span> is modulation index </p><p>Output signal-to-noise ratio (of AM receiver) is given by </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 \mathrm {(SNR)_{O,AM}} ={\frac {A_{c}^{2}k_{a}^{2}P}{2WN_{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">R</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">O</mi> <mo>,</mo> <mi mathvariant="normal">A</mi> <mi mathvariant="normal">M</mi> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <msubsup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mi>P</mi> </mrow> <mrow> <mn>2</mn> <mi>W</mi> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {(SNR)_{O,AM}} ={\frac {A_{c}^{2}k_{a}^{2}P}{2WN_{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dffb051cfd1a93fd0fb1d76985a89dadb8e0a0d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:22.054ex; height:6.009ex;" alt="{\displaystyle \mathrm {(SNR)_{O,AM}} ={\frac {A_{c}^{2}k_{a}^{2}P}{2WN_{0}}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Frequency_modulation">Frequency modulation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal-to-noise_ratio&action=edit&section=8" title="Edit section: Frequency modulation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Channel signal-to-noise ratio is given by </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 \mathrm {(SNR)_{C,FM}} ={\frac {A_{c}^{2}}{2WN_{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">R</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">C</mi> <mo>,</mo> <mi mathvariant="normal">F</mi> <mi mathvariant="normal">M</mi> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mrow> <mn>2</mn> <mi>W</mi> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {(SNR)_{C,FM}} ={\frac {A_{c}^{2}}{2WN_{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ded20fec313d17678c39a2d1630895eed8c1a530" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:21.465ex; height:6.009ex;" alt="{\displaystyle \mathrm {(SNR)_{C,FM}} ={\frac {A_{c}^{2}}{2WN_{0}}}}"></span></dd></dl> <p>Output signal-to-noise ratio is given by </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 \mathrm {(SNR)_{O,FM}} ={\frac {A_{c}^{2}k_{f}^{2}P}{2N_{0}W^{3}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">R</mi> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">O</mi> <mo>,</mo> <mi mathvariant="normal">F</mi> <mi mathvariant="normal">M</mi> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <msubsup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mi>P</mi> </mrow> <mrow> <mn>2</mn> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msup> <mi>W</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {(SNR)_{O,FM}} ={\frac {A_{c}^{2}k_{f}^{2}P}{2N_{0}W^{3}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b620deb115cf8984e2d68229641a2576bf5594a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:22.683ex; height:7.009ex;" alt="{\displaystyle \mathrm {(SNR)_{O,FM}} ={\frac {A_{c}^{2}k_{f}^{2}P}{2N_{0}W^{3}}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Noise_reduction">Noise reduction</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal-to-noise_ratio&action=edit&section=9" title="Edit section: Noise reduction"><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:Analyse_thermo_gravimetrique_bruit.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Analyse_thermo_gravimetrique_bruit.png/220px-Analyse_thermo_gravimetrique_bruit.png" decoding="async" width="220" height="138" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Analyse_thermo_gravimetrique_bruit.png/330px-Analyse_thermo_gravimetrique_bruit.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Analyse_thermo_gravimetrique_bruit.png/440px-Analyse_thermo_gravimetrique_bruit.png 2x" data-file-width="875" data-file-height="548" /></a><figcaption>Recording from a <a href="/wiki/Thermogravimetric_analysis" title="Thermogravimetric analysis">thermogravimetric analysis</a> device with poor mechanical isolation; the middle of the plot shows lower noise due to reduced human activity at night.</figcaption></figure> <p>All real measurements are disturbed by noise. This includes <a href="/wiki/Electronic_noise" class="mw-redirect" title="Electronic noise">electronic noise</a>, but can also include external events that affect the measured phenomenon — wind, vibrations, the gravitational attraction of the moon, variations of temperature, variations of humidity, etc., depending on what is measured and of the sensitivity of the device. It is often possible to reduce the noise by controlling the environment. </p><p>Internal electronic noise of measurement systems can be reduced through the use of <a href="/wiki/Low-noise_amplifier" title="Low-noise amplifier">low-noise amplifiers</a>. </p><p>When the characteristics of the noise are known and are different from the signal, it is possible to use a <a href="/wiki/Filter_(signal_processing)" title="Filter (signal processing)">filter</a> to reduce the noise. For example, a <a href="/wiki/Lock-in_amplifier" title="Lock-in amplifier">lock-in amplifier</a> can extract a narrow bandwidth signal from broadband noise a million times stronger. </p><p>When the signal is constant or periodic and the noise is random, it is possible to enhance the SNR by <a href="/wiki/Signal_averaging" title="Signal averaging">averaging</a> the measurements. In this case the noise goes down as the square root of the number of averaged samples. </p> <div class="mw-heading mw-heading2"><h2 id="Digital_signals">Digital signals</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal-to-noise_ratio&action=edit&section=10" title="Edit section: Digital signals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When a measurement is digitized, the number of bits used to represent the measurement determines the maximum possible signal-to-noise ratio. This is because the minimum possible <a href="/wiki/Noise" title="Noise">noise</a> level is the <a href="/wiki/Error" title="Error">error</a> caused by the <a href="/wiki/Quantization_(signal_processing)" title="Quantization (signal processing)">quantization</a> of the signal, sometimes called <a href="/wiki/Quantization_noise" class="mw-redirect" title="Quantization noise">quantization noise</a>. This noise level is non-linear and signal-dependent; different calculations exist for different signal models. Quantization noise is modeled as an analog error signal summed with the signal before quantization ("additive noise"). </p><p>This theoretical maximum SNR assumes a perfect input signal. If the input signal is already noisy (as is usually the case), the signal's noise may be larger than the quantization noise. Real <a href="/wiki/Analog-to-digital_converter" title="Analog-to-digital converter">analog-to-digital converters</a> also have other sources of noise that further decrease the SNR compared to the theoretical maximum from the idealized quantization noise, including the intentional addition of <a href="/wiki/Dither" title="Dither">dither</a>. </p><p>Although noise levels in a digital system can be expressed using SNR, it is more common to use <a href="/wiki/Eb/N0" title="Eb/N0">E<sub>b</sub>/N<sub>o</sub></a>, the energy per bit per noise power spectral density. </p><p>The <a href="/wiki/Modulation_error_ratio" title="Modulation error ratio">modulation error ratio</a> (MER) is a measure of the SNR in a digitally modulated signal. </p> <div class="mw-heading mw-heading3"><h3 id="Fixed_point">Fixed point</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal-to-noise_ratio&action=edit&section=11" title="Edit section: Fixed point"><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">See also: <a href="/wiki/Fixed-point_arithmetic" title="Fixed-point arithmetic">Fixed-point arithmetic</a></div> <p>For <i>n</i>-bit integers with equal distance between quantization levels (<a href="/wiki/Quantization_(signal_processing)" title="Quantization (signal processing)">uniform quantization</a>) the <a href="/wiki/Dynamic_range" title="Dynamic range">dynamic range</a> (DR) is also determined. </p><p>Assuming a uniform distribution of input signal values, the quantization noise is a uniformly distributed random signal with a peak-to-peak amplitude of one quantization level, making the amplitude ratio 2<sup><i>n</i></sup>/1. The formula is then: </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 \mathrm {DR_{dB}} =\mathrm {SNR_{dB}} =20\log _{10}(2^{n})\approx 6.02\cdot n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">D</mi> <msub> <mi mathvariant="normal">R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> </msub> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">N</mi> <msub> <mi mathvariant="normal">R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> </msub> </mrow> <mo>=</mo> <mn>20</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo stretchy="false">)</mo> <mo>≈</mo> <mn>6.02</mn> <mo>⋅</mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {DR_{dB}} =\mathrm {SNR_{dB}} =20\log _{10}(2^{n})\approx 6.02\cdot n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dca343a8a38b0fcda38cc5946242183b512921f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:41.106ex; height:2.843ex;" alt="{\displaystyle \mathrm {DR_{dB}} =\mathrm {SNR_{dB}} =20\log _{10}(2^{n})\approx 6.02\cdot n}"></span></dd></dl> <p>This relationship is the origin of statements like "<a href="/wiki/16-bit_audio" class="mw-redirect" title="16-bit audio">16-bit audio</a> has a dynamic range of 96 dB". Each extra quantization bit increases the dynamic range by roughly 6 dB. </p><p>Assuming a <a href="/wiki/Full-scale" class="mw-redirect" title="Full-scale">full-scale</a> <a href="/wiki/Sine_wave" title="Sine wave">sine wave</a> signal (that is, the quantizer is designed such that it has the same minimum and maximum values as the input signal), the quantization noise approximates a <a href="/wiki/Sawtooth_wave" title="Sawtooth wave">sawtooth wave</a> with peak-to-peak amplitude of one quantization level<sup id="cite_ref-maxim_728_14-0" class="reference"><a href="#cite_note-maxim_728-14"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> and uniform distribution. In this case, the SNR is approximately </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 \mathrm {SNR_{dB}} \approx 20\log _{10}(2^{n}{\textstyle {\sqrt {3/2}}})\approx 6.02\cdot n+1.761}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">N</mi> <msub> <mi mathvariant="normal">R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> </msub> </mrow> <mo>≈</mo> <mn>20</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mo stretchy="false">(</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <mo stretchy="false">)</mo> <mo>≈</mo> <mn>6.02</mn> <mo>⋅</mo> <mi>n</mi> <mo>+</mo> <mn>1.761</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {SNR_{dB}} \approx 20\log _{10}(2^{n}{\textstyle {\sqrt {3/2}}})\approx 6.02\cdot n+1.761}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/93701248e6b96bbfb0399bc4e17bb541ef2089d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:46.159ex; height:3.343ex;" alt="{\displaystyle \mathrm {SNR_{dB}} \approx 20\log _{10}(2^{n}{\textstyle {\sqrt {3/2}}})\approx 6.02\cdot n+1.761}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Floating_point">Floating point</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal-to-noise_ratio&action=edit&section=12" title="Edit section: Floating point"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Floating-point_numbers" class="mw-redirect" title="Floating-point numbers">Floating-point numbers</a> provide a way to trade off signal-to-noise ratio for an increase in dynamic range. For n-bit floating-point numbers, with n-m bits in the <a href="/wiki/Logarithm" title="Logarithm">mantissa</a> and m bits in the <a href="/wiki/Exponent" class="mw-redirect" title="Exponent">exponent</a>: </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 \mathrm {DR_{dB}} =6.02\cdot 2^{m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">D</mi> <msub> <mi mathvariant="normal">R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> </msub> </mrow> <mo>=</mo> <mn>6.02</mn> <mo>⋅</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {DR_{dB}} =6.02\cdot 2^{m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35dc3a59d3210d3ebea032d4d43d11bcd83f1d46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.545ex; height:2.676ex;" alt="{\displaystyle \mathrm {DR_{dB}} =6.02\cdot 2^{m}}"></span></dd></dl> <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 \mathrm {SNR_{dB}} =6.02\cdot (n-m)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">N</mi> <msub> <mi mathvariant="normal">R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> </msub> </mrow> <mo>=</mo> <mn>6.02</mn> <mo>⋅</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {SNR_{dB}} =6.02\cdot (n-m)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e9570b83a8ebde8fc7c5c94eee0d3d765b4a332" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.053ex; height:2.843ex;" alt="{\displaystyle \mathrm {SNR_{dB}} =6.02\cdot (n-m)}"></span></dd></dl> <p>The dynamic range is much larger than fixed-point but at a cost of a worse signal-to-noise ratio. This makes floating-point preferable in situations where the dynamic range is large or unpredictable. Fixed-point's simpler implementations can be used with no signal quality disadvantage in systems where dynamic range is less than 6.02m. The very large dynamic range of floating-point can be a disadvantage, since it requires more forethought in designing algorithms.<sup id="cite_ref-rane_fixed_vs_floating_15-0" class="reference"><a href="#cite_note-rane_fixed_vs_floating-15"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>note 3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>note 4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Optical_signals">Optical signals</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal-to-noise_ratio&action=edit&section=13" title="Edit section: Optical signals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Optical signals have a <a href="/wiki/Carrier_frequency" class="mw-redirect" title="Carrier frequency">carrier frequency</a> (about <span class="nowrap"><span data-sort-value="7014200000000000000♠"></span>200 THz</span> and more) that is much higher than the modulation frequency. This way the noise covers a bandwidth that is much wider than the signal itself. The resulting signal influence relies mainly on the filtering of the noise. To describe the signal quality without taking the receiver into account, the optical SNR (OSNR) is used. The OSNR is the ratio between the signal power and the noise power in a given bandwidth. Most commonly a reference bandwidth of 0.1 nm is used. This bandwidth is independent of the modulation format, the frequency and the receiver. For instance an OSNR of 20 dB/0.1 nm could be given, even the signal of 40 GBit <a href="/wiki/DPSK#Differential_phase-shift_keying_(DPSK)" class="mw-redirect" title="DPSK">DPSK</a> would not fit in this bandwidth. OSNR is measured with an <a href="/wiki/Optical_spectrum_analyzer" class="mw-redirect" title="Optical spectrum analyzer">optical spectrum analyzer</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Types_and_abbreviations">Types and abbreviations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal-to-noise_ratio&action=edit&section=14" title="Edit section: Types and abbreviations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Signal to noise ratio may be abbreviated as SNR and less commonly as S/N. PSNR stands for <a href="/wiki/Peak_signal-to-noise_ratio" title="Peak signal-to-noise ratio">peak signal-to-noise ratio</a>. GSNR stands for geometric signal-to-noise ratio.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> SINR is the <a href="/wiki/Signal-to-interference-plus-noise_ratio" title="Signal-to-interference-plus-noise ratio">signal-to-interference-plus-noise ratio</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Other_uses">Other uses</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal-to-noise_ratio&action=edit&section=15" title="Edit section: Other uses"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>While SNR is commonly quoted for electrical signals, it can be applied to any form of signal, for example <a href="/wiki/Isotope" title="Isotope">isotope</a> levels in an <a href="/wiki/Ice_core" title="Ice core">ice core</a>, <a href="/wiki/Biochemical_signaling" class="mw-redirect" title="Biochemical signaling">biochemical signaling</a> between cells, or <a href="/wiki/Financial_signal_processing" title="Financial signal processing">financial trading signals</a>. The term is sometimes used metaphorically to refer to the ratio of useful <a href="/wiki/Information" title="Information">information</a> to false or irrelevant data in a conversation or exchange. For example, in <a href="/wiki/Internet_forum" title="Internet forum">online discussion forums</a> and other online communities, <a href="/wiki/Off-topic" class="mw-redirect" title="Off-topic">off-topic</a> posts and <a href="/wiki/Spamming" title="Spamming">spam</a> are regarded as <em>noise</em> that interferes with the <em>signal</em> of appropriate discussion.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>SNR can also be applied in marketing and how business professionals manage information overload. Managing a healthy signal to noise ratio can help business executives improve their KPIs (Key Performance Indicators).<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Similar_concepts">Similar concepts</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal-to-noise_ratio&action=edit&section=16" title="Edit section: Similar concepts"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The signal-to-noise ratio is similar to <a href="/wiki/Cohen%27s_d" class="mw-redirect" title="Cohen's d">Cohen's d</a> given by the difference of estimated means divided by the standard deviation of the data <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 d={\frac {{\bar {X}}_{1}-{\bar {X}}_{2}}{\text{SD}}}={\frac {{\bar {X}}_{1}-{\bar {X}}_{2}}{\sigma }}={\frac {t}{\sqrt {N}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>X</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>X</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mtext>SD</mtext> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>X</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>X</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mi>σ</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>t</mi> <msqrt> <mi>N</mi> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d={\frac {{\bar {X}}_{1}-{\bar {X}}_{2}}{\text{SD}}}={\frac {{\bar {X}}_{1}-{\bar {X}}_{2}}{\sigma }}={\frac {t}{\sqrt {N}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9655e3c2ceb890376867bc2bb9205eaad0d9dc6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:34.837ex; height:6.676ex;" alt="{\displaystyle d={\frac {{\bar {X}}_{1}-{\bar {X}}_{2}}{\text{SD}}}={\frac {{\bar {X}}_{1}-{\bar {X}}_{2}}{\sigma }}={\frac {t}{\sqrt {N}}}}"></span> and is related to the <a href="/wiki/Test_statistic" title="Test statistic">test statistic</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 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> in the <a href="/wiki/T-test" class="mw-redirect" title="T-test">t-test</a>.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <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-to-noise_ratio&action=edit&section=17" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 20em;"> <ul><li><a href="/wiki/Audio_system_measurements" title="Audio system measurements">Audio system measurements</a></li> <li><a href="/wiki/Generation_loss" title="Generation loss">Generation loss</a></li> <li><a href="/wiki/Matched_filter" title="Matched filter">Matched filter</a></li> <li><a href="/wiki/Near%E2%80%93far_problem" title="Near–far problem">Near–far problem</a></li> <li><a href="/wiki/Noise_margin" title="Noise margin">Noise margin</a></li> <li><a href="/wiki/Omega_ratio" title="Omega ratio">Omega ratio</a></li> <li><a href="/wiki/Pareidolia" title="Pareidolia">Pareidolia</a></li> <li><a href="/wiki/Peak_signal-to-noise_ratio" title="Peak signal-to-noise ratio">Peak signal-to-noise ratio</a></li> <li><a href="/wiki/Signal-to-noise_statistic" title="Signal-to-noise statistic">Signal-to-noise statistic</a></li> <li><a href="/wiki/Signal-to-interference-plus-noise_ratio" title="Signal-to-interference-plus-noise ratio">Signal-to-interference-plus-noise ratio</a></li> <li><a href="/wiki/SINAD" title="SINAD">SINAD</a></li> <li><a href="/wiki/SINADR" title="SINADR">SINADR</a></li> <li><a href="/wiki/Subjective_video_quality" title="Subjective video quality">Subjective video quality</a></li> <li><a href="/wiki/Total_harmonic_distortion" title="Total harmonic distortion">Total harmonic distortion</a></li> <li><a href="/wiki/Video_quality" title="Video quality">Video quality</a></li></ul> </div> <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-to-noise_ratio&action=edit&section=18" 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-columns references-column-width"> <ol class="references"> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">The connection between <a href="/wiki/Optical_power" title="Optical power">optical power</a> and <a href="/wiki/Voltage" title="Voltage">voltage</a> in an imaging system is linear. This usually means that the SNR of the electrical signal is calculated by the <i>10 log</i> rule. With an <a href="/wiki/Interferometric" class="mw-redirect" title="Interferometric">interferometric</a> system, however, where interest lies in the signal from one arm only, the field of the electromagnetic wave is proportional to the voltage (assuming that the intensity in the second, the reference arm is constant). Therefore the optical power of the measurement arm is directly proportional to the electrical power and electrical signals from optical interferometry are following the <a href="/wiki/20_log_rule" class="mw-redirect" title="20 log rule"><i>20 log</i> rule</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></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">The exact methods may vary between fields. For example, if the signal data are known to be constant, then <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 \sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" 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 \sigma }"></span> can be calculated using the standard deviation of the signal. If the signal data are not constant, then <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 \sigma }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f59b7c3e6fdb1d0365a494b81fb9a696138c36" 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 \sigma }"></span> can be calculated from data where the signal is zero or relatively constant.</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">Often special filters are used to weight the noise: DIN-A, DIN-B, DIN-C, DIN-D, CCIR-601; for video, special filters such as <a href="/wiki/Comb_filter" title="Comb filter">comb filters</a> may be used.</span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">Maximum possible full scale signal can be charged as peak-to-peak or as RMS. Audio uses RMS, Video P-P, which gave +9 dB more SNR for video.</span> </li> </ol></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-to-noise_ratio&action=edit&section=19" 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-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFCharles_ShermanJohn_Butler2007" class="citation book cs1">Charles Sherman; John Butler (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=srREi-ScbFcC&q=%22signal+to+noise+ratio%22+define+mean-square&pg=PA276"><i>Transducers and Arrays for Underwater Sound</i></a>. Springer Science & Business Media. p. 276. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780387331393" title="Special:BookSources/9780387331393"><bdi>9780387331393</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Transducers+and+Arrays+for+Underwater+Sound&rft.pages=276&rft.pub=Springer+Science+%26+Business+Media&rft.date=2007&rft.isbn=9780387331393&rft.au=Charles+Sherman&rft.au=John+Butler&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DsrREi-ScbFcC%26q%3D%2522signal%2Bto%2Bnoise%2Bratio%2522%2Bdefine%2Bmean-square%26pg%3DPA276&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal-to-noise+ratio" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Michael A. Choma, Marinko V. Sarunic, Changhuei Yang, Joseph A. Izatt. <a rel="nofollow" class="external text" href="https://www.osapublishing.org/oe/fulltext.cfm?uri=oe-11-18-2183">Sensitivity advantage of swept source and Fourier domain optical coherence tomography</a>. Optics Express, 11(18). Sept 2003.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.sinoseen.com/what-is-signal-to-noise-ratiohow-does-it-effect-embedded-vision">"What is Signal-to-Noise Ratio？How does it effect Embedded Vision？"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-11-23</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=What+is+Signal-to-Noise+Ratio%EF%BC%9FHow+does+it+effect+Embedded+Vision%EF%BC%9F&rft_id=https%3A%2F%2Fwww.sinoseen.com%2Fwhat-is-signal-to-noise-ratiohow-does-it-effect-embedded-vision&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal-to-noise+ratio" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGabriel_L._A._de_SousaGeorge_C._Cardoso2018" class="citation journal cs1">Gabriel L. A. de Sousa; George C. Cardoso (18 June 2018). <a rel="nofollow" class="external text" href="https://doi.org/10.1088/1361-6552/aac84b">"A battery-resistor analogy for further insights on measurement uncertainties"</a>. <i>Physics Education</i>. <b>53</b> (5). IOP Publishing: 055001. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1611.03425">1611.03425</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2018PhyEd..53e5001D">2018PhyEd..53e5001D</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1088%2F1361-6552%2Faac84b">10.1088/1361-6552/aac84b</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:125414987">125414987</a><span class="reference-accessdate">. Retrieved <span class="nowrap">5 May</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Education&rft.atitle=A+battery-resistor+analogy+for+further+insights+on+measurement+uncertainties&rft.volume=53&rft.issue=5&rft.pages=055001&rft.date=2018-06-18&rft_id=info%3Aarxiv%2F1611.03425&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A125414987%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1088%2F1361-6552%2Faac84b&rft_id=info%3Abibcode%2F2018PhyEd..53e5001D&rft.au=Gabriel+L.+A.+de+Sousa&rft.au=George+C.+Cardoso&rft_id=https%3A%2F%2Fdoi.org%2F10.1088%2F1361-6552%2Faac84b&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal-to-noise+ratio" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFD._J._Schroeder1999" class="citation book cs1">D. 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Academic Press. p. 278. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-629810-9" title="Special:BookSources/978-0-12-629810-9"><bdi>978-0-12-629810-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Astronomical+optics&rft.pages=278&rft.edition=2nd&rft.pub=Academic+Press&rft.date=1999&rft.isbn=978-0-12-629810-9&rft.au=D.+J.+Schroeder&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dv7E25646wz0C%26pg%3DPA433&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal-to-noise+ratio" class="Z3988"></span>, <a rel="nofollow" class="external text" href="https://books.google.com/books?id=VZvqqaQ5DvoC&q=signal%20to%20noise&pg=PA278">p.278</a></span> </li> <li id="cite_note-b1-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-b1_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-b1_7-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Bushberg, J. T., et al., <i><a rel="nofollow" class="external text" href="https://books.google.com/books?id=VZvqqaQ5DvoC&pg=PA280">The Essential Physics of Medical Imaging</a>,</i> (2e). Philadelphia: Lippincott Williams & Wilkins, 2006, p. 280.</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="CITEREFRafael_C._González,_Richard_Eugene_Woods2008" class="citation book cs1">Rafael C. González, Richard Eugene Woods (2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=8uGOnjRGEzoC&pg=PA354"><i>Digital image processing</i></a>. Prentice Hall. p. 354. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-13-168728-8" title="Special:BookSources/978-0-13-168728-8"><bdi>978-0-13-168728-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Digital+image+processing&rft.pages=354&rft.pub=Prentice+Hall&rft.date=2008&rft.isbn=978-0-13-168728-8&rft.au=Rafael+C.+Gonz%C3%A1lez%2C+Richard+Eugene+Woods&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D8uGOnjRGEzoC%26pg%3DPA354&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal-to-noise+ratio" 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="CITEREFTania_Stathaki2008" class="citation book cs1">Tania Stathaki (2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=VmvY4MTMFTwC&pg=PA471"><i>Image fusion: algorithms and applications</i></a>. Academic Press. p. 471. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-372529-5" title="Special:BookSources/978-0-12-372529-5"><bdi>978-0-12-372529-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Image+fusion%3A+algorithms+and+applications&rft.pages=471&rft.pub=Academic+Press&rft.date=2008&rft.isbn=978-0-12-372529-5&rft.au=Tania+Stathaki&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DVmvY4MTMFTwC%26pg%3DPA471&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal-to-noise+ratio" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJitendra_R._Raol2009" class="citation book cs1">Jitendra R. Raol (2009). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=7s8xpR-5rOUC&pg=PA471"><i>Multi-Sensor Data Fusion: Theory and Practice</i></a>. CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4398-0003-4" title="Special:BookSources/978-1-4398-0003-4"><bdi>978-1-4398-0003-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Multi-Sensor+Data+Fusion%3A+Theory+and+Practice&rft.pub=CRC+Press&rft.date=2009&rft.isbn=978-1-4398-0003-4&rft.au=Jitendra+R.+Raol&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D7s8xpR-5rOUC%26pg%3DPA471&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal-to-noise+ratio" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJohn_C._Russ2007" class="citation book cs1">John C. Russ (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Vs2AM2cWl1AC&pg=PA26"><i>The image processing handbook</i></a>. CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-8493-7254-4" title="Special:BookSources/978-0-8493-7254-4"><bdi>978-0-8493-7254-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+image+processing+handbook&rft.pub=CRC+Press&rft.date=2007&rft.isbn=978-0-8493-7254-4&rft.au=John+C.+Russ&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DVs2AM2cWl1AC%26pg%3DPA26&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal-to-noise+ratio" 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="CITEREFRose1973" class="citation book cs1">Rose, Albert (1973). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/visionhumanelect01rose"><i>Vision – Human and Electronic</i></a></span>. Plenum Press. p. <a rel="nofollow" class="external text" href="https://archive.org/details/visionhumanelect01rose/page/10">10</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780306307324" title="Special:BookSources/9780306307324"><bdi>9780306307324</bdi></a>. <q>[...] to reduce the number of false alarms to below unity, we will need [...] a signal whose amplitude is 4–5 times larger than the rms noise.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Vision+%E2%80%93+Human+and+Electronic&rft.pages=10&rft.pub=Plenum+Press&rft.date=1973&rft.isbn=9780306307324&rft.aulast=Rose&rft.aufirst=Albert&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fvisionhumanelect01rose&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal-to-noise+ratio" class="Z3988"></span></span> </li> <li id="cite_note-maxim_728-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-maxim_728_14-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.maxim-ic.com/appnotes.cfm/appnote_number/728">Defining and Testing Dynamic Parameters in High-Speed ADCs</a> — <a href="/wiki/Maxim_Integrated_Products" class="mw-redirect" title="Maxim Integrated Products">Maxim Integrated Products</a> Application note 728</span> </li> <li id="cite_note-rane_fixed_vs_floating-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-rane_fixed_vs_floating_15-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060515074349/http://www.rane.com/note153.html">Fixed-Point vs. Floating-Point DSP for Superior Audio</a> — <a href="/wiki/Rane_Corporation" title="Rane Corporation">Rane Corporation</a> technical library</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTomasz_Pander2013" class="citation book cs1">Tomasz Pander (2013). <a rel="nofollow" class="external text" href="https://link.springer.com/chapter/10.1007/978-3-319-02309-0_28">"An Application of Myriad M-Estimator for Robust Weighted Averaging"</a>. <i>Man-Machine Interactions 3</i>. Advances in Intelligent Systems and Computing. Vol. 242. ICMMI. pp. 265–272. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-319-02309-0_28">10.1007/978-3-319-02309-0_28</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783319023090" title="Special:BookSources/9783319023090"><bdi>9783319023090</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=An+Application+of+Myriad+M-Estimator+for+Robust+Weighted+Averaging&rft.btitle=Man-Machine+Interactions+3&rft.series=Advances+in+Intelligent+Systems+and+Computing&rft.pages=265-272&rft.pub=ICMMI&rft.date=2013&rft_id=info%3Adoi%2F10.1007%2F978-3-319-02309-0_28&rft.isbn=9783319023090&rft.au=Tomasz+Pander&rft_id=https%3A%2F%2Flink.springer.com%2Fchapter%2F10.1007%2F978-3-319-02309-0_28&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal-to-noise+ratio" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBreeding2004" class="citation book cs1">Breeding, Andy (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=W5bAcxc2TcgC&pg=PA128"><i>The Music Internet Untangled: Using Online Services to Expand Your Musical Horizons</i></a>. Giant Path. p. 128. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781932340020" title="Special:BookSources/9781932340020"><bdi>9781932340020</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+Music+Internet+Untangled%3A+Using+Online+Services+to+Expand+Your+Musical+Horizons&rft.pages=128&rft.pub=Giant+Path&rft.date=2004&rft.isbn=9781932340020&rft.aulast=Breeding&rft.aufirst=Andy&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DW5bAcxc2TcgC%26pg%3DPA128&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal-to-noise+ratio" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</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.thruways.co/blog/what-is-signal-to-noise-ratio">"What Is Signal To Noise Ratio?"</a>. <i>www.thruways.co</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2023-11-09</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.thruways.co&rft.atitle=What+Is+Signal+To+Noise+Ratio%3F&rft_id=https%3A%2F%2Fwww.thruways.co%2Fblog%2Fwhat-is-signal-to-noise-ratio&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal-to-noise+ratio" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</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://blog.minitab.com/en/adventures-in-statistics-2/understanding-t-tests-1-sample-2-sample-and-paired-t-tests">"Understanding t-Tests: 1-sample, 2-sample, and Paired t-Tests"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-08-19</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Understanding+t-Tests%3A+1-sample%2C+2-sample%2C+and+Paired+t-Tests&rft_id=https%3A%2F%2Fblog.minitab.com%2Fen%2Fadventures-in-statistics-2%2Funderstanding-t-tests-1-sample-2-sample-and-paired-t-tests&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal-to-noise+ratio" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Signal-to-noise_ratio&action=edit&section=20" title="Edit section: External links"><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="CITEREFWalt_Kester" class="citation cs2">Walt Kester, <a rel="nofollow" class="external text" href="http://www.analog.com/static/imported-files/tutorials/MT-001.pdf"><i>Taking the Mystery out of the Infamous Formula,"SNR = 6.02N + 1.76dB," and Why You Should Care</i></a> <span class="cs1-format">(PDF)</span>, Analog Devices, <a rel="nofollow" class="external text" href="https://ghostarchive.org/archive/20221009/http://www.analog.com/static/imported-files/tutorials/MT-001.pdf">archived</a> <span class="cs1-format">(PDF)</span> from the original on 2022-10-09<span class="reference-accessdate">, retrieved <span class="nowrap">2019-04-10</span></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Taking+the+Mystery+out+of+the+Infamous+Formula%2C%22SNR+%3D+6.02N+%2B+1.76dB%2C%22+and+Why+You+Should+Care&rft.pub=Analog+Devices&rft.au=Walt+Kester&rft_id=http%3A%2F%2Fwww.analog.com%2Fstatic%2Fimported-files%2Ftutorials%2FMT-001.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal-to-noise+ratio" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://www.maxim-ic.com/appnotes.cfm/appnote_number/641">ADC and DAC Glossary</a> – <a href="/wiki/Maxim_Integrated_Products" class="mw-redirect" title="Maxim Integrated Products">Maxim Integrated Products</a></li> <li><a rel="nofollow" class="external text" href="http://www.analog.com/static/imported-files/tutorials/MT-003.pdf">Understand SINAD, ENOB, SNR, THD, THD + N, and SFDR so you don't get lost in the noise floor</a> – <a href="/wiki/Analog_Devices" title="Analog Devices">Analog Devices</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060522134626/http://www.techonline.com/community/related_content/20771">The Relationship of dynamic range to data word size in digital audio processing</a></li> <li><a rel="nofollow" class="external text" href="http://www.sengpielaudio.com/calculator-noise.htm">Calculation of signal-to-noise ratio, noise voltage, and noise level</a></li> <li><a rel="nofollow" class="external text" href="http://www.vias.org/simulations/simusoft_spectaccu.html">Learning by simulations – a simulation showing the improvement of the SNR by time averaging</a></li> <li><a rel="nofollow" class="external text" href="http://focus.ti.com/lit/an/sbaa055/sbaa055.pdf">Dynamic Performance Testing of Digital Audio D/A Converters</a></li> <li><a rel="nofollow" class="external text" href="http://www.circuitdesign.info/blog/2008/11/fundamentals-of-analogrf-design-noise-signal-power/">Fundamental theorem of analog circuits: a minimum level of power must be dissipated to maintain a level of SNR</a></li> <li><a rel="nofollow" class="external text" href="http://webdemo.inue.uni-stuttgart.de/webdemos/02_lectures/uebertragungstechnik_1/qam_constellation_diagram_from_snr">Interactive webdemo of visualization of SNR in a QAM constellation diagram</a> Institute of Telecommunicatons, University of Stuttgart</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBernard_Widrow,_István_Kollár2008" class="citation cs2">Bernard Widrow, István Kollár (2008-07-03), <a rel="nofollow" class="external text" href="http://www.cambridge.org/9780521886710"><i>Quantization Noise: Roundoff Error in Digital Computation, Signal Processing, Control, and Communications</i></a>, Cambridge University Press, Cambridge, UK, 2008. 778 p., <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780521886710" title="Special:BookSources/9780521886710"><bdi>9780521886710</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Quantization+Noise%3A+Roundoff+Error+in+Digital+Computation%2C+Signal+Processing%2C+Control%2C+and+Communications&rft.pub=Cambridge+University+Press%2C+Cambridge%2C+UK%2C+2008.+778+p.&rft.date=2008-07-03&rft.isbn=9780521886710&rft.au=Bernard+Widrow%2C+Istv%C3%A1n+Koll%C3%A1r&rft_id=http%3A%2F%2Fwww.cambridge.org%2F9780521886710&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASignal-to-noise+ratio" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://oldweb.mit.bme.hu/books/quantization/">Quantization Noise</a> Widrow & Kollár Quantization book page with sample chapters and additional material</li> <li><a rel="nofollow" class="external text" href="https://www.etti.unibw.de/labalive/experiment/snr/">Signal-to-noise ratio online audio demonstrator - Virtual Communications Lab</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist 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.navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Noise_(physics_and_telecommunications)" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Noise" title="Template:Noise"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Noise" title="Template talk:Noise"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Noise" title="Special:EditPage/Template:Noise"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Noise_(physics_and_telecommunications)" style="font-size:114%;margin:0 4em"><a href="/wiki/Noise_(spectral_phenomenon)" title="Noise (spectral phenomenon)">Noise</a> (physics and telecommunications)</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Acoustic_quieting" title="Acoustic quieting">Acoustic quieting</a></li> <li><a href="/wiki/Distortion" title="Distortion">Distortion</a></li> <li><a href="/wiki/Active_noise_control" title="Active noise control">Noise cancellation</a></li> <li><a href="/wiki/Noise_control" title="Noise control">Noise control</a></li> <li><a href="/wiki/Noise_measurement" title="Noise measurement">Noise measurement</a></li> <li><a href="/wiki/Noise_power" title="Noise power">Noise power</a></li> <li><a href="/wiki/Noise_reduction" title="Noise reduction">Noise reduction</a></li> <li><a href="/wiki/Noise_temperature" title="Noise temperature">Noise temperature</a></li> <li><a href="/wiki/Phase_distortion" title="Phase distortion">Phase distortion</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Noise in...</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Noise" title="Noise">Audio</a></li> <li><a href="/wiki/Architectural_acoustics" title="Architectural acoustics">Buildings</a></li> <li><a href="/wiki/Noise_(electronics)" title="Noise (electronics)">Electronics</a></li> <li><a href="/wiki/Noise_pollution" title="Noise pollution">Environment</a></li> <li><a href="/wiki/Noise_regulation" title="Noise regulation">Government regulation</a></li> <li><a href="/wiki/Health_effects_from_noise" title="Health effects from noise">Human health</a></li> <li><a href="/wiki/Image_noise" title="Image noise">Images</a></li> <li><a href="/wiki/Noise_(radio)" class="mw-redirect" title="Noise (radio)">Radio</a></li> <li><a href="/wiki/Soundproofing" title="Soundproofing">Rooms</a></li> <li><a href="/wiki/Noise_and_vibration_on_maritime_vessels" title="Noise and vibration on maritime vessels">Ships</a></li> <li><a href="/wiki/Sound_masking" title="Sound masking">Sound masking</a></li> <li><a href="/wiki/Noise_barrier" title="Noise barrier">Transportation</a></li> <li><a href="/wiki/Noise_(video)" title="Noise (video)">Video</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Class of noise</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Additive_white_Gaussian_noise" title="Additive white Gaussian noise">Additive white Gaussian noise</a> (AWGN)</li> <li><a href="/wiki/Atmospheric_noise" title="Atmospheric noise">Atmospheric noise</a></li> <li><a href="/wiki/Background_noise" title="Background noise">Background noise</a></li> <li><a href="/wiki/Brownian_noise" title="Brownian noise">Brownian noise</a></li> <li><a href="/wiki/Burst_noise" title="Burst noise">Burst noise</a></li> <li><a href="/wiki/Cosmic_noise" title="Cosmic noise">Cosmic noise</a></li> <li><a href="/wiki/Flicker_noise" title="Flicker noise">Flicker noise</a></li> <li><a href="/wiki/Gaussian_noise" title="Gaussian noise">Gaussian noise</a></li> <li><a href="/wiki/Grey_noise" title="Grey noise">Grey noise</a></li> <li><a href="/wiki/Infrasound" title="Infrasound">Infrasound</a></li> <li><a href="/wiki/Jitter" title="Jitter">Jitter</a></li> <li><a href="/wiki/Johnson%E2%80%93Nyquist_noise" title="Johnson–Nyquist noise">Johnson–Nyquist noise</a> (thermal noise)</li> <li><a href="/wiki/Pink_noise" title="Pink noise">Pink noise</a></li> <li><a href="/wiki/Quantization_error" class="mw-redirect" title="Quantization error">Quantization error</a> (or q. noise)</li> <li><a href="/wiki/Shot_noise" title="Shot noise">Shot noise</a></li> <li><a href="/wiki/White_noise" title="White noise">White noise</a></li> <li>Coherent noise <ul><li><a href="/wiki/Value_noise" title="Value noise">Value noise</a></li> <li><a href="/wiki/Gradient_noise" title="Gradient noise">Gradient noise</a></li> <li><a href="/wiki/Worley_noise" title="Worley noise">Worley noise</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Engineering <br />terms</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Channel_noise_level" title="Channel noise level">Channel noise level</a></li> <li><a href="/wiki/Circuit_noise_level" title="Circuit noise level">Circuit noise level</a></li> <li><a href="/wiki/Effective_input_noise_temperature" title="Effective input noise temperature">Effective input noise temperature</a></li> <li><a href="/wiki/Equivalent_noise_resistance" title="Equivalent noise resistance">Equivalent noise resistance</a></li> <li><a href="/wiki/Equivalent_pulse_code_modulation_noise" title="Equivalent pulse code modulation noise">Equivalent pulse code modulation noise</a></li> <li><a href="/wiki/Impulse_noise_(audio)" class="mw-redirect" title="Impulse noise (audio)">Impulse noise (audio)</a></li> <li><a href="/wiki/Noise_figure" title="Noise figure">Noise figure</a></li> <li><a href="/wiki/Noise_floor" title="Noise floor">Noise floor</a></li> <li><a href="/wiki/Noise_shaping" title="Noise shaping">Noise shaping</a></li> <li><a href="/wiki/Noise_spectral_density" title="Noise spectral density">Noise spectral density</a></li> <li><a href="/wiki/Noise,_vibration,_and_harshness" title="Noise, vibration, and harshness">Noise, vibration, and harshness</a> (NVH)</li> <li><a href="/wiki/Phase_noise" title="Phase noise">Phase noise</a></li> <li><a href="/wiki/Pseudorandom_noise" title="Pseudorandom noise">Pseudorandom noise</a></li> <li><a href="/wiki/Statistical_noise" class="mw-redirect" title="Statistical noise">Statistical noise</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Ratios</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Carrier-to-noise_ratio" title="Carrier-to-noise ratio">Carrier-to-noise ratio</a> (<i>C</i>/<i>N</i>)</li> <li><a href="/wiki/Carrier-to-receiver_noise_density" class="mw-redirect" title="Carrier-to-receiver noise density">Carrier-to-receiver noise density</a> (<i>C</i>/<i>kT</i>)</li> <li><i><a href="/wiki/DBrnC" class="mw-redirect" title="DBrnC">dBrnC</a></i></li> <li><i><a href="/wiki/Eb/N0" title="Eb/N0">E<sub>b</sub>/N<sub>0</sub></a></i> (energy per bit to noise density)</li> <li><i><a href="/wiki/Eb/N0#Relation_to_Es.2FN0" title="Eb/N0">E<sub>s</sub>/N<sub>0</sub></a></i> (energy per symbol to noise density)</li> <li><a href="/wiki/Modulation_error_ratio" title="Modulation error ratio">Modulation error ratio</a> (<i>MER</i>)</li> <li><a href="/wiki/SINAD" title="SINAD">Signal, noise and distortion</a> (<i>SINAD</i>)</li> <li><a href="/wiki/Signal-to-interference_ratio" title="Signal-to-interference ratio">Signal-to-interference ratio</a> (<i>S</i>/<i>I</i>)</li> <li><a class="mw-selflink selflink">Signal-to-noise ratio</a> (<i>S</i>/<i>N</i>, <i>SNR</i>)</li> <li><a href="/wiki/Signal-to-noise_ratio_(imaging)" title="Signal-to-noise ratio (imaging)">Signal-to-noise ratio (imaging)</a></li> <li><a href="/wiki/Signal-to-interference-plus-noise_ratio" title="Signal-to-interference-plus-noise ratio">Signal-to-interference-plus-noise ratio</a> (<i>SINR</i>)</li> <li><a href="/wiki/Signal-to-quantization-noise_ratio" title="Signal-to-quantization-noise ratio">Signal-to-quantization-noise ratio</a> (<i>SQNR</i>)</li> <li><a href="/wiki/Contrast-to-noise_ratio" title="Contrast-to-noise ratio">Contrast-to-noise ratio</a> (<i>CNR</i>)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_noise_topics" title="List of noise topics">List of noise topics</a></li> <li><a href="/wiki/Acoustics" title="Acoustics">Acoustics</a></li> <li><a href="/wiki/Colors_of_noise" title="Colors of noise">Colors of noise</a></li> <li><a href="/wiki/Interference_(communication)" title="Interference (communication)">Interference (communication)</a></li> <li><a href="/wiki/Noise_generator" title="Noise generator">Noise generator</a></li> <li><a href="/wiki/Spectrum_analyzer" title="Spectrum analyzer">Spectrum analyzer</a></li> <li><a href="/wiki/Thermal_radiation" title="Thermal radiation">Thermal radiation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Denoise <br />methods</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Low-pass_filter" title="Low-pass filter">Low-pass filter</a></li> <li><a href="/wiki/Median_filter" title="Median filter">Median filter</a></li> <li><a href="/wiki/Total_variation_denoising" title="Total variation denoising">Total variation denoising</a></li> <li><a href="/wiki/Wavelet#Wavelet_denoising" title="Wavelet">Wavelet denoising</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">2D (Image)</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Gaussian_blur" title="Gaussian blur">Gaussian blur</a></li> <li><a href="/wiki/Anisotropic_diffusion" title="Anisotropic diffusion">Anisotropic diffusion</a></li> <li><a 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