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class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Z-plane_analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Z-plane analysis</span> </div> </a> <ul id="toc-Z-plane_analysis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Autoregression_analysis" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Autoregression_analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Autoregression analysis</span> </div> </a> <ul id="toc-Autoregression_analysis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Time-frequency_analysis" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Time-frequency_analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Time-frequency analysis</span> </div> </a> <ul id="toc-Time-frequency_analysis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Wavelet" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Wavelet"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Wavelet</span> </div> </a> <ul id="toc-Wavelet-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Empirical_mode_decomposition" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Empirical_mode_decomposition"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.7</span> <span>Empirical mode decomposition</span> </div> </a> <ul id="toc-Empirical_mode_decomposition-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Implementation" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Implementation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Implementation</span> </div> </a> <ul id="toc-Implementation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Applications</span> </div> </a> <ul id="toc-Applications-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Techniques" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Techniques"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Techniques</span> </div> </a> <ul id="toc-Techniques-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Related_fields" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Related_fields"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Related fields</span> </div> </a> <ul id="toc-Related_fields-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Software_Tools_for_Digital_Signal_Processing" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Software_Tools_for_Digital_Signal_Processing"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Software Tools for Digital Signal Processing</span> </div> </a> <button aria-controls="toc-Software_Tools_for_Digital_Signal_Processing-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 Software Tools for Digital Signal Processing subsection</span> </button> <ul id="toc-Software_Tools_for_Digital_Signal_Processing-sublist" class="vector-toc-list"> <li id="toc-1._MATLAB" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#1._MATLAB"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>1. MATLAB</span> </div> </a> <ul id="toc-1._MATLAB-sublist" class="vector-toc-list"> <li id="toc-Overview" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Overview"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1.1</span> <span>Overview</span> </div> </a> <ul id="toc-Overview-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Key_Features" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Key_Features"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1.2</span> <span>Key Features</span> </div> </a> <ul id="toc-Key_Features-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications_2" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Applications_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1.3</span> <span>Applications</span> </div> </a> <ul id="toc-Applications_2-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-2._Python_(with_NumPy_and_SciPy)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#2._Python_(with_NumPy_and_SciPy)"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>2. Python (with NumPy and SciPy)</span> </div> </a> <ul id="toc-2._Python_(with_NumPy_and_SciPy)-sublist" class="vector-toc-list"> <li id="toc-Overview_2" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Overview_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2.1</span> <span>Overview</span> </div> </a> <ul id="toc-Overview_2-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Key_Features_2" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Key_Features_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2.2</span> <span>Key Features</span> </div> </a> <ul id="toc-Key_Features_2-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications_3" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Applications_3"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2.3</span> <span>Applications</span> </div> </a> <ul id="toc-Applications_3-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-3._LabVIEW" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#3._LabVIEW"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3</span> <span>3. LabVIEW</span> </div> </a> <ul id="toc-3._LabVIEW-sublist" class="vector-toc-list"> <li id="toc-Overview_3" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Overview_3"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3.1</span> <span>Overview</span> </div> </a> <ul id="toc-Overview_3-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Key_Features_3" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Key_Features_3"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3.2</span> <span>Key Features</span> </div> </a> <ul id="toc-Key_Features_3-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications_4" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Applications_4"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3.3</span> <span>Applications</span> </div> </a> <ul id="toc-Applications_4-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-4._GNU_Radio" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#4._GNU_Radio"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.4</span> <span>4. GNU Radio</span> </div> </a> <ul id="toc-4._GNU_Radio-sublist" class="vector-toc-list"> <li id="toc-Overview_4" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Overview_4"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.4.1</span> <span>Overview</span> </div> </a> <ul id="toc-Overview_4-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Key_Features_4" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Key_Features_4"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.4.2</span> <span>Key Features</span> </div> </a> <ul id="toc-Key_Features_4-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications_5" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Applications_5"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.4.3</span> <span>Applications</span> </div> </a> <ul id="toc-Applications_5-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-5._Octave" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#5._Octave"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.5</span> <span>5. Octave</span> </div> </a> <ul id="toc-5._Octave-sublist" class="vector-toc-list"> <li id="toc-Overview_5" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Overview_5"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.5.1</span> <span>Overview</span> </div> </a> <ul id="toc-Overview_5-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Key_Features_5" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Key_Features_5"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.5.2</span> <span>Key Features</span> </div> </a> <ul id="toc-Key_Features_5-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications_6" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Applications_6"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.5.3</span> <span>Applications</span> </div> </a> <ul id="toc-Applications_6-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-6._C/C++_with_DSP_Libraries" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#6._C/C++_with_DSP_Libraries"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.6</span> <span>6. C/C++ with DSP Libraries</span> </div> </a> <ul id="toc-6._C/C++_with_DSP_Libraries-sublist" class="vector-toc-list"> <li id="toc-Overview_6" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Overview_6"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.6.1</span> <span>Overview</span> </div> </a> <ul id="toc-Overview_6-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Key_Features_6" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Key_Features_6"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.6.2</span> <span>Key Features</span> </div> </a> <ul id="toc-Key_Features_6-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications_7" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Applications_7"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.6.3</span> <span>Applications</span> </div> </a> <ul id="toc-Applications_7-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Conclusion" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Conclusion"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Conclusion</span> </div> </a> <ul id="toc-Conclusion-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>References</span> </div> </a> <ul id="toc-References-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">Digital signal processing</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 39 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-39" 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">39 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%85%D8%B9%D8%A7%D9%84%D8%AC%D8%A9_%D8%B1%D9%82%D9%85%D9%8A%D8%A9_%D9%84%D9%84%D8%A5%D8%B4%D8%A7%D8%B1%D8%A9" title="معالجة رقمية للإشارة – Arabic" lang="ar" hreflang="ar" data-title="معالجة رقمية للإشارة" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Processament_de_senyals_digitals" title="Processament de senyals digitals – Catalan" lang="ca" hreflang="ca" data-title="Processament de senyals digitals" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Digital_signalbehandling" title="Digital signalbehandling – Danish" lang="da" hreflang="da" data-title="Digital signalbehandling" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Digitale_Signalverarbeitung" title="Digitale Signalverarbeitung – German" lang="de" hreflang="de" data-title="Digitale Signalverarbeitung" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Digitaalne_signaalit%C3%B6%C3%B6tlus" title="Digitaalne signaalitöötlus – Estonian" lang="et" hreflang="et" data-title="Digitaalne signaalitöötlus" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A8%CE%B7%CF%86%CE%B9%CE%B1%CE%BA%CE%AE_%CE%B5%CF%80%CE%B5%CE%BE%CE%B5%CF%81%CE%B3%CE%B1%CF%83%CE%AF%CE%B1_%CF%83%CE%AE%CE%BC%CE%B1%CF%84%CE%BF%CF%82" title="Ψηφιακή επεξεργασία σήματος – Greek" lang="el" hreflang="el" data-title="Ψηφιακή επεξεργασία σήματος" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Procesamiento_digital_de_se%C3%B1ales" title="Procesamiento digital de señales – Spanish" lang="es" hreflang="es" data-title="Procesamiento digital de señales" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%BE%D8%B1%D8%AF%D8%A7%D8%B2%D8%B4_%D8%B3%DB%8C%DA%AF%D9%86%D8%A7%D9%84_%D8%AF%DB%8C%D8%AC%DB%8C%D8%AA%D8%A7%D9%84" title="پردازش سیگنال دیجیتال – Persian" lang="fa" hreflang="fa" data-title="پردازش سیگنال دیجیتال" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Traitement_num%C3%A9rique_du_signal" title="Traitement numérique du signal – French" lang="fr" hreflang="fr" data-title="Traitement numérique du signal" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Procesado_dixital_de_sinais" title="Procesado dixital de sinais – Galician" lang="gl" hreflang="gl" data-title="Procesado dixital de sinais" 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/%EB%94%94%EC%A7%80%ED%84%B8_%EC%8B%A0%ED%98%B8_%EC%B2%98%EB%A6%AC" title="디지털 신호 처리 – Korean" lang="ko" hreflang="ko" data-title="디지털 신호 처리" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%85%E0%A4%82%E0%A4%95%E0%A5%80%E0%A4%AF_%E0%A4%B8%E0%A4%82%E0%A4%95%E0%A5%87%E0%A4%A4_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%95%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A4%A3" title="अंकीय संकेत प्रक्रमण – Hindi" lang="hi" hreflang="hi" data-title="अंकीय संकेत प्रक्रमण" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Pengolahan_sinyal_digital" title="Pengolahan sinyal digital – Indonesian" lang="id" hreflang="id" data-title="Pengolahan sinyal digital" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Ukudludlungwa_kwesiyabizo_sezezibhangqiwe" title="Ukudludlungwa kwesiyabizo sezezibhangqiwe – Zulu" lang="zu" hreflang="zu" data-title="Ukudludlungwa kwesiyabizo sezezibhangqiwe" data-language-autonym="IsiZulu" data-language-local-name="Zulu" class="interlanguage-link-target"><span>IsiZulu</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Elaborazione_numerica_dei_segnali" title="Elaborazione numerica dei segnali – Italian" lang="it" hreflang="it" data-title="Elaborazione numerica dei segnali" 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%A2%D7%99%D7%91%D7%95%D7%93_%D7%90%D7%95%D7%AA%D7%95%D7%AA_%D7%A1%D7%A4%D7%A8%D7%AA%D7%99" title="עיבוד אותות ספרתי – Hebrew" lang="he" hreflang="he" data-title="עיבוד אותות ספרתי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A4%D0%B0%D0%B7%D0%B0%D0%BB%D1%8B%D2%9B_%D1%82%D1%8B%D2%93%D1%8B%D0%B7%D0%B4%D0%B0%D1%83" title="Фазалық тығыздау – Kazakh" lang="kk" hreflang="kk" data-title="Фазалық тығыздау" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Digit%C3%A1lis_jelfeldolgoz%C3%A1s" title="Digitális jelfeldolgozás – Hungarian" lang="hu" hreflang="hu" data-title="Digitális jelfeldolgozás" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a 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<div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Mathematical signal manipulation by computers</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Digital transform" redirects here. For the impact of digital technology on society, see <a href="/wiki/Digital_transformation" title="Digital transformation">Digital transformation</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed plainlinks metadata ambox ambox-content ambox-Refimprove" 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 article <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Digital_signal_processing" title="Special:EditPage/Digital signal processing">improve this article</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 removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Digital+signal+processing%22">"Digital signal processing"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Digital+signal+processing%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Digital+signal+processing%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Digital+signal+processing%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Digital+signal+processing%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Digital+signal+processing%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">May 2008</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><b>Digital signal processing</b> (<b>DSP</b>) is the use of <a href="/wiki/Digital_processing" class="mw-redirect" title="Digital processing">digital processing</a>, such as by computers or more specialized <a href="/wiki/Digital_signal_processor" title="Digital signal processor">digital signal processors</a>, to perform a wide variety of <a href="/wiki/Signal_processing" title="Signal processing">signal processing</a> operations. The <a href="/wiki/Digital_signal" title="Digital signal">digital signals</a> processed in this manner are a sequence of numbers that represent <a href="/wiki/Sampling_(signal_processing)" title="Sampling (signal processing)">samples</a> of a <a href="/wiki/Continuous_variable" class="mw-redirect" title="Continuous variable">continuous variable</a> in a domain such as time, space, or frequency. In <a href="/wiki/Digital_electronics" title="Digital electronics">digital electronics</a>, a digital signal is represented as a <a href="/wiki/Pulse_train" class="mw-redirect" title="Pulse train">pulse train</a>,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><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> which is typically generated by the switching of a <a href="/wiki/Transistor" title="Transistor">transistor</a>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Digital signal processing and <a href="/wiki/Analog_signal_processing" title="Analog signal processing">analog signal processing</a> are subfields of signal processing. DSP applications include <a href="/wiki/Audio_signal_processing" title="Audio signal processing">audio</a> and <a href="/wiki/Speech_processing" title="Speech processing">speech processing</a>, <a href="/wiki/Sonar" title="Sonar">sonar</a>, <a href="/wiki/Radar" title="Radar">radar</a> and other <a href="/wiki/Sensor_array" title="Sensor array">sensor array</a> processing, <a href="/wiki/Spectral_density_estimation" title="Spectral density estimation">spectral density estimation</a>, <a href="/wiki/Statistical_signal_processing" class="mw-redirect" title="Statistical signal processing">statistical signal processing</a>, <a href="/wiki/Digital_image_processing" title="Digital image processing">digital image processing</a>, <a href="/wiki/Data_compression" title="Data compression">data compression</a>, <a href="/wiki/Video_coding" class="mw-redirect" title="Video coding">video coding</a>, <a href="/wiki/Audio_coding" class="mw-redirect" title="Audio coding">audio coding</a>, <a href="/wiki/Image_compression" title="Image compression">image compression</a>, signal processing for <a href="/wiki/Telecommunications" title="Telecommunications">telecommunications</a>, <a href="/wiki/Control_system" title="Control system">control systems</a>, <a href="/wiki/Biomedical_engineering" title="Biomedical engineering">biomedical engineering</a>, and <a href="/wiki/Seismology" title="Seismology">seismology</a>, among others. </p><p>DSP can involve linear or nonlinear operations. Nonlinear signal processing is closely related to <a href="/wiki/Nonlinear_system_identification" title="Nonlinear system identification">nonlinear system identification</a><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> and can be implemented in the <a href="/wiki/Time_domain" title="Time domain">time</a>, <a href="/wiki/Frequency_domain" title="Frequency domain">frequency</a>, and <a href="/wiki/Spacetime" title="Spacetime">spatio-temporal domains</a>. </p><p>The application of digital computation to signal processing allows for many advantages over analog processing in many applications, such as <a href="/wiki/Error_detection_and_correction" title="Error detection and correction">error detection and correction</a> in transmission as well as <a href="/wiki/Data_compression" title="Data compression">data compression</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Digital signal processing is also fundamental to <a href="/wiki/Digital_electronics" title="Digital electronics">digital technology</a>, such as <a href="/wiki/Digital_telecommunication" class="mw-redirect" title="Digital telecommunication">digital telecommunication</a> and <a href="/wiki/Wireless_communications" class="mw-redirect" title="Wireless communications">wireless communications</a>.<sup id="cite_ref-Srivastava_6-0" class="reference"><a href="#cite_note-Srivastava-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> DSP is applicable to both <a href="/wiki/Streaming_data" title="Streaming data">streaming data</a> and static (stored) data. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Signal_sampling">Signal sampling</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=1" title="Edit section: Signal sampling"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Sampling_(signal_processing)" title="Sampling (signal processing)">Sampling (signal processing)</a></div> <p>To digitally analyze and manipulate an analog signal, it must be digitized with an <a href="/wiki/Analog-to-digital_converter" title="Analog-to-digital converter">analog-to-digital converter</a> (ADC).<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Sampling is usually carried out in two stages, <a href="/wiki/Discretization" title="Discretization">discretization</a> and <a href="/wiki/Quantization_(signal_processing)" title="Quantization (signal processing)">quantization</a>. Discretization means that the signal is divided into equal intervals of time, and each interval is represented by a single measurement of amplitude. Quantization means each amplitude measurement is approximated by a value from a finite set. Rounding <a href="/wiki/Real_numbers" class="mw-redirect" title="Real numbers">real numbers</a> to integers is an example. </p><p>The <a href="/wiki/Nyquist%E2%80%93Shannon_sampling_theorem" title="Nyquist–Shannon sampling theorem">Nyquist–Shannon sampling theorem</a> states that a signal can be exactly reconstructed from its samples if the sampling frequency is greater than twice the highest frequency component in the signal. In practice, the sampling frequency is often significantly higher than this.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> It is common to use an <a href="/wiki/Anti-aliasing_filter" title="Anti-aliasing filter">anti-aliasing filter</a> to limit the signal bandwidth to comply with the sampling theorem, however careful selection of this filter is required because the reconstructed signal will be the filtered signal plus residual <a href="/wiki/Aliasing" title="Aliasing">aliasing</a> from imperfect <a href="/wiki/Stop_band" class="mw-redirect" title="Stop band">stop band</a> rejection instead of the original (unfiltered) signal. </p><p>Theoretical DSP analyses and derivations are typically performed on <a href="/wiki/Discrete-time_signal" class="mw-redirect" title="Discrete-time signal">discrete-time signal</a> models with no amplitude inaccuracies (<a href="/wiki/Quantization_error" class="mw-redirect" title="Quantization error">quantization error</a>), created by the abstract process of <a href="/wiki/Sampling_(signal_processing)" title="Sampling (signal processing)">sampling</a>. Numerical methods require a quantized signal, such as those produced by an ADC. The processed result might be a frequency spectrum or a set of statistics. But often it is another quantized signal that is converted back to analog form by a <a href="/wiki/Digital-to-analog_converter" title="Digital-to-analog converter">digital-to-analog converter</a> (DAC). </p> <div class="mw-heading mw-heading2"><h2 id="Domains">Domains</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=2" title="Edit section: Domains"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>DSP engineers usually study digital signals in one of the following domains: <a href="/wiki/Time_domain" title="Time domain">time domain</a> (one-dimensional signals), spatial domain (multidimensional signals), <a href="/wiki/Frequency_domain" title="Frequency domain">frequency domain</a>, and <a href="/wiki/Wavelet" title="Wavelet">wavelet</a> domains. They choose the domain in which to process a signal by making an informed assumption (or by trying different possibilities) as to which domain best represents the essential characteristics of the signal and the processing to be applied to it. A sequence of samples from a measuring device produces a temporal or spatial domain representation, whereas a <a href="/wiki/Discrete_Fourier_transform" title="Discrete Fourier transform">discrete Fourier transform</a> produces the frequency domain representation. </p> <div class="mw-heading mw-heading3"><h3 id="Time_and_space_domains">Time and space domains</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=3" title="Edit section: Time and space domains"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Time_domain" title="Time domain">Time domain</a> refers to the analysis of signals with respect to time. Similarly, space domain refers to the analysis of signals with respect to position, e.g., pixel location for the case of image processing. </p><p>The most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering. <a href="/wiki/Digital_filter" title="Digital filter">Digital filtering</a> generally consists of some linear transformation of a number of surrounding samples around the current sample of the input or output signal. The surrounding samples may be identified with respect to time or space. The output of a linear digital filter to any given input may be calculated by <a href="/wiki/Convolution" title="Convolution">convolving</a> the input signal with an <a href="/wiki/Impulse_response" title="Impulse response">impulse response</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Frequency_domain">Frequency domain</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=4" title="Edit section: Frequency domain"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Frequency_domain" title="Frequency domain">Frequency domain</a></div> <p>Signals are converted from time or space domain to the frequency domain usually through use of the <a href="/wiki/Fourier_transform" title="Fourier transform">Fourier transform</a>. The Fourier transform converts the time or space information to a magnitude and phase component of each frequency. With some applications, how the phase varies with frequency can be a significant consideration. Where phase is unimportant, often the Fourier transform is converted to the power spectrum, which is the magnitude of each frequency component squared. </p><p>The most common purpose for analysis of signals in the frequency domain is analysis of signal properties. The engineer can study the spectrum to determine which frequencies are present in the input signal and which are missing. Frequency domain analysis is also called <i>spectrum-</i> or <i>spectral analysis</i>. </p><p>Filtering, particularly in non-realtime work can also be achieved in the frequency domain, applying the filter and then converting back to the time domain. This can be an efficient implementation and can give essentially any filter response including excellent approximations to <a href="/wiki/Brickwall_filter" class="mw-redirect" title="Brickwall filter">brickwall filters</a>. </p><p>There are some commonly used frequency domain transformations. For example, the <a href="/wiki/Cepstrum" title="Cepstrum">cepstrum</a> converts a signal to the frequency domain through Fourier transform, takes the logarithm, then applies another Fourier transform. This emphasizes the harmonic structure of the original spectrum. </p> <div class="mw-heading mw-heading3"><h3 id="Z-plane_analysis">Z-plane analysis</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=5" title="Edit section: Z-plane analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Digital filters come in both <a href="/wiki/Infinite_impulse_response" title="Infinite impulse response">infinite impulse response</a> (IIR) and <a href="/wiki/Finite_impulse_response" title="Finite impulse response">finite impulse response</a> (FIR) types. Whereas FIR filters are always stable, IIR filters have feedback loops that may become unstable and oscillate. The <a href="/wiki/Z-transform" title="Z-transform">Z-transform</a> provides a tool for analyzing stability issues of digital IIR filters. It is analogous to the <a href="/wiki/Laplace_transform" title="Laplace transform">Laplace transform</a>, which is used to design and analyze analog IIR filters. </p> <div class="mw-heading mw-heading3"><h3 id="Autoregression_analysis">Autoregression analysis</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=6" title="Edit section: Autoregression analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A signal is represented as linear combination of its previous samples. Coefficients of the combination are called autoregression coefficients. This method has higher frequency resolution and can process shorter signals compared to the Fourier transform.<sup id="cite_ref-Marple_9-0" class="reference"><a href="#cite_note-Marple-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Prony%27s_method" title="Prony's method">Prony's method</a> can be used to estimate phases, amplitudes, initial phases and decays of the components of signal.<sup id="cite_ref-Ribeiro_10-0" class="reference"><a href="#cite_note-Ribeiro-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Marple_9-1" class="reference"><a href="#cite_note-Marple-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Components are assumed to be complex decaying exponents.<sup id="cite_ref-Ribeiro_10-1" class="reference"><a href="#cite_note-Ribeiro-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Marple_9-2" class="reference"><a href="#cite_note-Marple-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Time-frequency_analysis">Time-frequency analysis</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=7" title="Edit section: Time-frequency analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A time-frequency representation of signal can capture both temporal evolution and frequency structure of analyzed signal. Temporal and frequency resolution are limited by the principle of uncertainty and the tradeoff is adjusted by the width of analysis window. Linear techniques such as <a href="/wiki/Short-time_Fourier_transform" title="Short-time Fourier transform">Short-time Fourier transform</a>, <a href="/wiki/Wavelet_transform" title="Wavelet transform">wavelet transform</a>, <a href="/wiki/Filter_bank" title="Filter bank">filter bank</a>,<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> non-linear (e.g., <a href="/w/index.php?title=Wigner%E2%80%93Ville_transform&action=edit&redlink=1" class="new" title="Wigner–Ville transform (page does not exist)">Wigner–Ville transform</a><sup id="cite_ref-Ribeiro_10-2" class="reference"><a href="#cite_note-Ribeiro-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>) and <a href="/wiki/Autoregressive" class="mw-redirect" title="Autoregressive">autoregressive</a> methods (e.g. segmented Prony method)<sup id="cite_ref-Ribeiro_10-3" class="reference"><a href="#cite_note-Ribeiro-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> are used for representation of signal on the time-frequency plane. Non-linear and segmented Prony methods can provide higher resolution, but may produce undesirable artifacts. Time-frequency analysis is usually used for analysis of non-stationary signals. For example, methods of <a href="/wiki/Fundamental_frequency" title="Fundamental frequency">fundamental frequency</a> estimation, such as RAPT and PEFAC<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> are based on windowed spectral analysis. </p> <div class="mw-heading mw-heading3"><h3 id="Wavelet">Wavelet</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=8" title="Edit section: Wavelet"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Jpeg2000_2-level_wavelet_transform-lichtenstein.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Jpeg2000_2-level_wavelet_transform-lichtenstein.png/300px-Jpeg2000_2-level_wavelet_transform-lichtenstein.png" decoding="async" width="300" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Jpeg2000_2-level_wavelet_transform-lichtenstein.png/450px-Jpeg2000_2-level_wavelet_transform-lichtenstein.png 1.5x, //upload.wikimedia.org/wikipedia/commons/e/e0/Jpeg2000_2-level_wavelet_transform-lichtenstein.png 2x" data-file-width="512" data-file-height="512" /></a><figcaption>An example of the 2D discrete wavelet transform that is used in <a href="/wiki/JPEG2000" class="mw-redirect" title="JPEG2000">JPEG2000</a>. The original image is high-pass filtered, yielding the three large images, each describing local changes in brightness (details) in the original image. It is then low-pass filtered and downscaled, yielding an approximation image; this image is high-pass filtered to produce the three smaller detail images, and low-pass filtered to produce the final approximation image in the upper-left.</figcaption></figure> <p>In <a href="/wiki/Numerical_analysis" title="Numerical analysis">numerical analysis</a> and <a href="/wiki/Functional_analysis" title="Functional analysis">functional analysis</a>, a <a href="/wiki/Discrete_wavelet_transform" title="Discrete wavelet transform">discrete wavelet transform</a> is any <a href="/wiki/Wavelet_transform" title="Wavelet transform">wavelet transform</a> for which the <a href="/wiki/Wavelet" title="Wavelet">wavelets</a> are discretely sampled. As with other wavelet transforms, a key advantage it has over <a href="/wiki/Fourier_transform" title="Fourier transform">Fourier transforms</a> is temporal resolution: it captures both frequency <i>and</i> location information. The accuracy of the joint time-frequency resolution is limited by the <a href="/wiki/Uncertainty_principle#Signal_processing" title="Uncertainty principle">uncertainty principle</a> of time-frequency. </p> <div class="mw-heading mw-heading3"><h3 id="Empirical_mode_decomposition">Empirical mode decomposition</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=9" title="Edit section: Empirical mode decomposition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Empirical mode decomposition is based on decomposition signal into <a href="/wiki/Intrinsic_mode_function" class="mw-redirect" title="Intrinsic mode function">intrinsic mode functions</a> (IMFs). IMFs are quasiharmonical oscillations that are extracted from the signal.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Implementation">Implementation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=10" title="Edit section: Implementation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>DSP <a href="/wiki/Algorithm" title="Algorithm">algorithms</a> may be run on general-purpose computers<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Digital_signal_processor" title="Digital signal processor">digital signal processors</a>.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> DSP algorithms are also implemented on purpose-built hardware such as <a href="/wiki/Application-specific_integrated_circuit" title="Application-specific integrated circuit">application-specific integrated circuit</a> (ASICs).<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Additional technologies for digital signal processing include more powerful general purpose <a href="/wiki/Microprocessor" title="Microprocessor">microprocessors</a>, <a href="/wiki/Graphics_processing_unit" title="Graphics processing unit">graphics processing units</a>, <a href="/wiki/Field-programmable_gate_array" title="Field-programmable gate array">field-programmable gate arrays</a> (FPGAs), <a href="/wiki/Digital_signal_controller" title="Digital signal controller">digital signal controllers</a> (mostly for industrial applications such as motor control), and <a href="/wiki/Stream_processing" title="Stream processing">stream processors</a>.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p><p>For systems that do not have a <a href="/wiki/Real-time_computing" title="Real-time computing">real-time computing</a> requirement and the signal data (either input or output) exists in data files, processing may be done economically with a general-purpose computer. This is essentially no different from any other <a href="/wiki/Data_processing" title="Data processing">data processing</a>, except DSP mathematical techniques (such as the <a href="/wiki/Discrete_cosine_transform" title="Discrete cosine transform">DCT</a> and <a href="/wiki/FFT" class="mw-redirect" title="FFT">FFT</a>) are used, and the sampled data is usually assumed to be uniformly sampled in time or space. An example of such an application is processing <a href="/wiki/Digital_photograph" class="mw-redirect" title="Digital photograph">digital photographs</a> with software such as <a href="/wiki/Photoshop" class="mw-redirect" title="Photoshop">Photoshop</a>. </p><p>When the application requirement is real-time, DSP is often implemented using specialized or dedicated processors or microprocessors, sometimes using multiple processors or multiple processing cores. These may process data using fixed-point arithmetic or floating point. For more demanding applications <a href="/wiki/FPGA" class="mw-redirect" title="FPGA">FPGAs</a> may be used.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> For the most demanding applications or high-volume products, <a href="/wiki/ASIC" class="mw-redirect" title="ASIC">ASICs</a> might be designed specifically for the application. </p><p>Parallel implementations of DSP algorithms, utilising multi-core CPU and many-core GPU architectures, are developed to improve the performances in terms of latency of these algorithms.<sup id="cite_ref-:0_21-0" class="reference"><a href="#cite_note-:0-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p><p><b><style data-mw-deduplicate="TemplateStyles:r1238216509">.mw-parser-output .vanchor>:target~.vanchor-text{background-color:#b1d2ff}@media screen{html.skin-theme-clientpref-night .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .vanchor>:target~.vanchor-text{background-color:#0f4dc9}}</style><span class="vanchor"><span id="Native_processing"></span><span class="vanchor-text">Native processing</span></span></b> is done by the computer's CPU rather than by DSP or outboard processing, which is done by additional third-party DSP chips located on extension cards or external hardware boxes or racks. Many <a href="/wiki/Digital_audio_workstation" title="Digital audio workstation">digital audio workstations</a> such as <a href="/wiki/Logic_Pro" title="Logic Pro">Logic Pro</a>, <a href="/wiki/Cubase" class="mw-redirect" title="Cubase">Cubase</a>, <a href="/wiki/Digital_Performer" title="Digital Performer">Digital Performer</a> and <a href="/wiki/Pro_Tools" title="Pro Tools">Pro Tools</a> LE use native processing. Others, such as <a href="/wiki/Pro_Tools" title="Pro Tools">Pro Tools</a> HD, <a href="/wiki/Universal_Audio_(company)" title="Universal Audio (company)">Universal Audio</a>'s UAD-1 and <a href="/wiki/TC_Electronic" title="TC Electronic">TC Electronic</a>'s Powercore use DSP processing. </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=11" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>General application areas for DSP include </p> <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_signal_processing" title="Audio signal processing">Audio signal processing</a></li> <li><a href="/wiki/Audio_data_compression" class="mw-redirect" title="Audio data compression">Audio data compression</a> e.g. <a href="/wiki/MP3" title="MP3">MP3</a></li> <li><a href="/wiki/Video_data_compression" class="mw-redirect" title="Video data compression">Video data compression</a></li> <li><a href="/wiki/Computer_graphics" title="Computer graphics">Computer graphics</a></li> <li><a href="/wiki/Digital_image_processing" title="Digital image processing">Digital image processing</a></li> <li><a href="/wiki/Photo_manipulation" class="mw-redirect" title="Photo manipulation">Photo manipulation</a></li> <li><a href="/wiki/Speech_processing" title="Speech processing">Speech processing</a></li> <li><a href="/wiki/Speech_recognition" title="Speech recognition">Speech recognition</a></li> <li><a href="/wiki/Data_transmission" class="mw-redirect" title="Data transmission">Data transmission</a></li> <li><a href="/wiki/Radar" title="Radar">Radar</a></li> <li><a href="/wiki/Sonar" title="Sonar">Sonar</a></li> <li><a href="/wiki/Financial_signal_processing" title="Financial signal processing">Financial signal processing</a></li> <li><a href="/wiki/Economic_forecasting" title="Economic forecasting">Economic forecasting</a></li> <li><a href="/wiki/Seismology" title="Seismology">Seismology</a></li> <li><a href="/wiki/Biomedicine" title="Biomedicine">Biomedicine</a></li> <li><a href="/wiki/Weather_forecasting" title="Weather forecasting">Weather forecasting</a></li></ul> </div> <p>Specific examples include <a href="/wiki/Speech_coding" title="Speech coding">speech coding</a> and transmission in digital <a href="/wiki/Mobile_phone" title="Mobile phone">mobile phones</a>, <a href="/wiki/Room_correction" class="mw-redirect" title="Room correction">room correction</a> of sound in <a href="/wiki/Hi-fi" class="mw-redirect" title="Hi-fi">hi-fi</a> and <a href="/wiki/Sound_reinforcement" class="mw-redirect" title="Sound reinforcement">sound reinforcement</a> applications, analysis and control of <a href="/wiki/Industrial_process" class="mw-redirect" title="Industrial process">industrial processes</a>, <a href="/wiki/Medical_imaging" title="Medical imaging">medical imaging</a> such as <a href="/wiki/Computed_axial_tomography" class="mw-redirect" title="Computed axial tomography">CAT</a> scans and <a href="/wiki/MRI" class="mw-redirect" title="MRI">MRI</a>, <a href="/wiki/Audio_crossover" title="Audio crossover">audio crossovers</a> and <a href="/wiki/Equalization_(audio)" title="Equalization (audio)">equalization</a>, <a href="/wiki/Digital_synthesizer" title="Digital synthesizer">digital synthesizers</a>, and audio <a href="/wiki/Effects_unit" title="Effects unit">effects units</a>.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> DSP has been used in <a href="/wiki/Hearing_aid" title="Hearing aid">hearing aid</a> technology since 1996, which allows for automatic directional microphones, complex digital <a href="/wiki/Noise_reduction" title="Noise reduction">noise reduction</a>, and improved adjustment of the <a href="/wiki/Frequency_response" title="Frequency response">frequency response</a>.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Techniques">Techniques</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=12" title="Edit section: Techniques"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><div class="div-col" style="column-width: 20em;"> <ul><li><a href="/wiki/Bilinear_transform" title="Bilinear transform">Bilinear transform</a></li> <li><a href="/wiki/Discrete_Fourier_transform" title="Discrete Fourier transform">Discrete Fourier transform</a></li> <li><a href="/wiki/Discrete-time_Fourier_transform" title="Discrete-time Fourier transform">Discrete-time Fourier transform</a></li> <li><a href="/wiki/Filter_design" title="Filter design">Filter design</a></li> <li><a href="/wiki/Goertzel_algorithm" title="Goertzel algorithm">Goertzel algorithm</a></li> <li><a href="/wiki/Least-squares_spectral_analysis" title="Least-squares spectral analysis">Least-squares spectral analysis</a></li> <li><a href="/wiki/LTI_system_theory" class="mw-redirect" title="LTI system theory">LTI system theory</a></li> <li><a href="/wiki/Minimum_phase" title="Minimum phase">Minimum phase</a></li> <li><a href="/wiki/S-plane" class="mw-redirect" title="S-plane">s-plane</a></li> <li><a href="/wiki/Transfer_function" title="Transfer function">Transfer function</a></li> <li><a href="/wiki/Z-transform" title="Z-transform">Z-transform</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Related_fields">Related fields</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=13" title="Edit section: Related fields"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><div class="div-col" style="column-width: 20em;"> <ul><li><a href="/wiki/Analog_signal_processing" title="Analog signal processing">Analog signal processing</a></li> <li><a href="/wiki/Automatic_control" class="mw-redirect" title="Automatic control">Automatic control</a></li> <li><a href="/wiki/Computer_engineering" title="Computer engineering">Computer engineering</a></li> <li><a href="/wiki/Computer_science" title="Computer science">Computer science</a></li> <li><a href="/wiki/Data_compression" title="Data compression">Data compression</a></li> <li><a href="/wiki/Dataflow_programming" title="Dataflow programming">Dataflow programming</a></li> <li><a href="/wiki/Discrete_cosine_transform" title="Discrete cosine transform">Discrete cosine transform</a></li> <li><a href="/wiki/Electrical_engineering" title="Electrical engineering">Electrical engineering</a></li> <li><a href="/wiki/Fourier_analysis" title="Fourier analysis">Fourier analysis</a></li> <li><a href="/wiki/Information_theory" title="Information theory">Information theory</a></li> <li><a href="/wiki/Machine_learning" title="Machine learning">Machine learning</a></li> <li><a href="/wiki/Real-time_computing" title="Real-time computing">Real-time computing</a></li> <li><a href="/wiki/Stream_processing" title="Stream processing">Stream processing</a></li> <li><a href="/wiki/Telecommunications" title="Telecommunications">Telecommunications</a></li> <li><a href="/wiki/Time_series" title="Time series">Time series</a></li> <li><a href="/wiki/Wavelet" title="Wavelet">Wavelet</a></li></ul> </div> <p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="Software_Tools_for_Digital_Signal_Processing">Software Tools for Digital Signal Processing</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=14" title="Edit section: Software Tools for Digital Signal Processing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Digital Signal Processing (DSP) involves the manipulation of signals after they have been converted into a digital format. This field is supported by a variety of software tools that enable engineers, researchers, and hobbyists to design, analyze, and implement DSP algorithms. This article explores some of the most popular software tools used in DSP, highlighting their features, advantages, and common applications. </p> <div class="mw-heading mw-heading3"><h3 id="1._MATLAB">1. MATLAB</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=15" title="Edit section: 1. MATLAB"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Overview">Overview</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=16" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>MATLAB (Matrix Laboratory) is one of the most widely used software tools for DSP. It offers a high-level programming environment with built-in functions for signal processing, making it accessible for both beginners and experts. </p> <div class="mw-heading mw-heading4"><h4 id="Key_Features">Key Features</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=17" title="Edit section: Key Features"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Toolboxes: The DSP System Toolbox provides functions for designing and simulating DSP systems.</li> <li>Visualization: Powerful plotting capabilities for analyzing signals and systems.</li> <li>Simulink: A graphical environment for modeling and simulating dynamic systems, including signal processing applications.</li></ul> <div class="mw-heading mw-heading4"><h4 id="Applications_2">Applications</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=18" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>MATLAB is used for research, algorithm development, and prototyping in various fields such as telecommunications, audio processing, and biomedical engineering. </p> <div class="mw-heading mw-heading3"><h3 id="2._Python_(with_NumPy_and_SciPy)"><span id="2._Python_.28with_NumPy_and_SciPy.29"></span>2. Python (with NumPy and SciPy)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=19" title="Edit section: 2. Python (with NumPy and SciPy)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Overview_2">Overview</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=20" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Python is an open-source programming language that has gained popularity in scientific computing. Libraries such as NumPy and SciPy extend Python’s capabilities for numerical computations and signal processing. </p> <div class="mw-heading mw-heading4"><h4 id="Key_Features_2">Key Features</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=21" title="Edit section: Key Features"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>NumPy: Provides support for large multi-dimensional arrays and matrices, along with mathematical functions to operate on them.</li> <li>SciPy: Offers additional functionality for signal processing, including filtering, window functions, and Fourier transforms.</li> <li>Matplotlib: A library for creating static, animated, and interactive visualizations in Python.</li></ul> <div class="mw-heading mw-heading4"><h4 id="Applications_3">Applications</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=22" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Python is widely used in research, machine learning, and data analysis, making it suitable for DSP applications in various domains. </p> <div class="mw-heading mw-heading3"><h3 id="3._LabVIEW">3. LabVIEW</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=23" title="Edit section: 3. LabVIEW"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Overview_3">Overview</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=24" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>LabVIEW (Laboratory Virtual Instrument Engineering Workbench) is a system-design platform and development environment from National Instruments. It is particularly popular in industry for automated testing and measurement. </p> <div class="mw-heading mw-heading4"><h4 id="Key_Features_3">Key Features</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=25" title="Edit section: Key Features"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Graphical Programming: Uses a visual programming language called G, making it intuitive for users.</li> <li>Integration: Seamlessly integrates with hardware for real-time data acquisition and analysis.</li> <li>Toolkits: Offers specialized toolkits for DSP applications, including the LabVIEW DSP Module.</li></ul> <div class="mw-heading mw-heading4"><h4 id="Applications_4">Applications</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=26" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>LabVIEW is commonly used in embedded systems, instrumentation, and control systems, particularly in industries like telecommunications and automotive. </p> <div class="mw-heading mw-heading3"><h3 id="4._GNU_Radio">4. GNU Radio</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=27" title="Edit section: 4. GNU Radio"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Overview_4">Overview</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=28" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>GNU Radio is an open-source software development toolkit that provides signal processing blocks to implement software-defined radios (SDRs) and signal processing systems. </p> <div class="mw-heading mw-heading4"><h4 id="Key_Features_4">Key Features</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=29" title="Edit section: Key Features"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Modular Design: Users can create complex signal processing flows using a graphical user interface or by writing Python scripts.</li> <li>Extensive Community: A strong community supports the development of new blocks and features.</li> <li>Real-Time Processing: Capable of real-time signal processing with SDR hardware.</li></ul> <div class="mw-heading mw-heading4"><h4 id="Applications_5">Applications</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=30" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>GNU Radio is used in academic research, prototyping of communication systems, and hobbyist projects involving radio and wireless communications. </p> <div class="mw-heading mw-heading3"><h3 id="5._Octave">5. Octave</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=31" title="Edit section: 5. Octave"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Overview_5">Overview</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=32" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>GNU Octave is an open-source alternative to MATLAB, providing a similar environment for numerical computations and signal processing. </p> <div class="mw-heading mw-heading4"><h4 id="Key_Features_5">Key Features</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=33" title="Edit section: Key Features"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>MATLAB Compatibility: Many MATLAB scripts can run in Octave with minimal modifications.</li> <li>Built-in Functions: Includes functions for DSP such as filtering, Fourier analysis, and more.</li> <li>Visualization: Offers plotting capabilities for signal analysis.</li></ul> <div class="mw-heading mw-heading4"><h4 id="Applications_6">Applications</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=34" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Octave is particularly useful for educational purposes, allowing students to learn DSP concepts without the cost of MATLAB. </p> <div class="mw-heading mw-heading3"><h3 id="6._C/C++_with_DSP_Libraries"><span id="6._C.2FC.2B.2B_with_DSP_Libraries"></span>6. C/C++ with DSP Libraries</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=35" title="Edit section: 6. C/C++ with DSP Libraries"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Overview_6">Overview</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=36" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For high-performance DSP applications, C and C++ are often used, especially when low-level control over hardware is required. Libraries such as Intel’s IPP (Integrated Performance Primitives) and ARM’s CMSIS-DSP provide optimized functions for signal processing. </p> <div class="mw-heading mw-heading4"><h4 id="Key_Features_6">Key Features</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=37" title="Edit section: Key Features"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Performance: Offers high performance for real-time applications due to low-level programming.</li> <li>Flexibility: Allows for custom implementation of algorithms tailored to specific applications.</li> <li>Access to Hardware: Direct access to hardware resources, which is crucial for embedded systems.</li></ul> <div class="mw-heading mw-heading4"><h4 id="Applications_7">Applications</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=38" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>C/C++ is used in applications requiring real-time processing, such as telecommunications, embedded systems, and video processing. </p> <div class="mw-heading mw-heading2"><h2 id="Conclusion">Conclusion</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=39" title="Edit section: Conclusion"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Digital signal processing is a versatile field supported by a wide array of software tools. From high-level environments like MATLAB and Python to low-level programming with C/C++, these tools cater to various needs, whether for research, education, or industry applications. As DSP continues to evolve, these software tools play a critical role in advancing the capabilities and efficiencies of signal processing technologies. </p> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Digital_signal_processing&action=edit&section=40" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/40px-Wikibooks-logo-en-noslogan.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/60px-Wikibooks-logo-en-noslogan.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/Wikibooks-logo-en-noslogan.svg/80px-Wikibooks-logo-en-noslogan.svg.png 2x" data-file-width="400" data-file-height="400" /></span></span></div> <div class="side-box-text plainlist">Wikibooks has a book on the topic of: <i><b><a href="https://en.wikibooks.org/wiki/Digital_Signal_Processing" class="extiw" title="wikibooks:Digital Signal Processing">Digital Signal Processing</a></b></i></div></div> </div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin refbegin-columns references-column-width" style="column-width: 30em"> <ul><li><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="CITEREFAhmedRao1975" class="citation book cs1"><a href="/wiki/Nasir_Ahmed_(engineer)" title="Nasir Ahmed (engineer)">Ahmed, Nasir</a>; <a href="/wiki/K._R._Rao" title="K. R. Rao">Rao, Kamisetty Ramamohan</a> (7 August 1975). "Orthogonal transforms for digital signal processing". <i>ICASSP '76. IEEE International Conference on Acoustics, Speech, and Signal Processing</i>. Vol. 1. New York: <a href="/wiki/Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer-Verlag</a>. pp. 136–140. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FICASSP.1976.1170121">10.1109/ICASSP.1976.1170121</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3540065562" title="Special:BookSources/978-3540065562"><bdi>978-3540065562</bdi></a>. <a href="/wiki/LCCN_(identifier)" class="mw-redirect" title="LCCN (identifier)">LCCN</a> <a rel="nofollow" class="external text" href="https://lccn.loc.gov/73018912">73018912</a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/438821458">438821458</a>. <a href="/wiki/OL_(identifier)" class="mw-redirect" title="OL (identifier)">OL</a> <a rel="nofollow" class="external text" href="https://openlibrary.org/books/OL22806004M">22806004M</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:10776771">10776771</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Orthogonal+transforms+for+digital+signal+processing&rft.btitle=ICASSP+%2776.+IEEE+International+Conference+on+Acoustics%2C+Speech%2C+and+Signal+Processing&rft.place=New+York&rft.pages=136-140&rft.pub=Springer-Verlag&rft.date=1975-08-07&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A10776771%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FICASSP.1976.1170121&rft_id=https%3A%2F%2Fopenlibrary.org%2Fbooks%2FOL22806004M%23id-name%3DOL&rft_id=info%3Alccn%2F73018912&rft_id=info%3Aoclcnum%2F438821458&rft.isbn=978-3540065562&rft.aulast=Ahmed&rft.aufirst=Nasir&rft.au=Rao%2C+Kamisetty+Ramamohan&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADigital+signal+processing" class="Z3988"></span></li> <li>Jonathan M. Blackledge, Martin Turner: <i>Digital Signal Processing: Mathematical and Computational Methods, Software Development and Applications</i>, Horwood Publishing, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-898563-48-9" title="Special:BookSources/1-898563-48-9">1-898563-48-9</a></li> <li>James D. Broesch: <i>Digital Signal Processing Demystified</i>, Newnes, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-878707-16-7" title="Special:BookSources/1-878707-16-7">1-878707-16-7</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDyerHarms1993" class="citation book cs1">Dyer, Stephen A.; Harms, Brian K. (13 August 1993). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=vL-bB7GALAwC&pg=PA104">"Digital Signal Processing"</a>. In Yovits, Marshall C. (ed.). <i>Advances in Computers</i>. Vol. 37. <a href="/wiki/Academic_Press" title="Academic Press">Academic Press</a>. pp. 59–118. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0065-2458%2808%2960403-9">10.1016/S0065-2458(08)60403-9</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0120121373" title="Special:BookSources/978-0120121373"><bdi>978-0120121373</bdi></a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0065-2458">0065-2458</a>. <a href="/wiki/LCCN_(identifier)" class="mw-redirect" title="LCCN (identifier)">LCCN</a> <a rel="nofollow" class="external text" href="https://lccn.loc.gov/59015761">59015761</a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/858439915">858439915</a>. <a href="/wiki/OL_(identifier)" class="mw-redirect" title="OL (identifier)">OL</a> <a rel="nofollow" class="external text" href="https://openlibrary.org/books/OL10070096M">10070096M</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Digital+Signal+Processing&rft.btitle=Advances+in+Computers&rft.pages=59-118&rft.pub=Academic+Press&rft.date=1993-08-13&rft_id=info%3Alccn%2F59015761&rft_id=info%3Adoi%2F10.1016%2FS0065-2458%2808%2960403-9&rft_id=https%3A%2F%2Fopenlibrary.org%2Fbooks%2FOL10070096M%23id-name%3DOL&rft.issn=0065-2458&rft_id=info%3Aoclcnum%2F858439915&rft.isbn=978-0120121373&rft.aulast=Dyer&rft.aufirst=Stephen+A.&rft.au=Harms%2C+Brian+K.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DvL-bB7GALAwC%26pg%3DPA104&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADigital+signal+processing" class="Z3988"></span></li> <li>Paul M. Embree, Damon Danieli: <i>C++ Algorithms for Digital Signal Processing</i>, Prentice Hall, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-13-179144-3" title="Special:BookSources/0-13-179144-3">0-13-179144-3</a></li> <li>Hari Krishna Garg: <i>Digital Signal Processing Algorithms</i>, CRC Press, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8493-7178-3" title="Special:BookSources/0-8493-7178-3">0-8493-7178-3</a></li> <li>P. Gaydecki: <i>Foundations Of Digital Signal Processing: Theory, Algorithms And Hardware Design</i>, Institution of Electrical Engineers, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-85296-431-5" title="Special:BookSources/0-85296-431-5">0-85296-431-5</a></li> <li>Ashfaq Khan: <i>Digital Signal Processing Fundamentals</i>, Charles River Media, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-58450-281-9" title="Special:BookSources/1-58450-281-9">1-58450-281-9</a></li> <li>Sen M. Kuo, Woon-Seng Gan: <i>Digital Signal Processors: Architectures, Implementations, and Applications</i>, Prentice Hall, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-13-035214-4" title="Special:BookSources/0-13-035214-4">0-13-035214-4</a></li> <li>Paul A. Lynn, Wolfgang Fuerst: <i>Introductory Digital Signal Processing with Computer Applications</i>, John Wiley & Sons, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-97984-8" title="Special:BookSources/0-471-97984-8">0-471-97984-8</a></li> <li>Richard G. Lyons: <i>Understanding Digital Signal Processing</i>, Prentice Hall, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-13-108989-7" title="Special:BookSources/0-13-108989-7">0-13-108989-7</a></li> <li>Vijay Madisetti, Douglas B. Williams: <i>The Digital Signal Processing Handbook</i>, CRC Press, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8493-8572-5" title="Special:BookSources/0-8493-8572-5">0-8493-8572-5</a></li> <li><a href="/wiki/James_H._McClellan" title="James H. McClellan">James H. McClellan</a>, <a href="/wiki/Ronald_W._Schafer" title="Ronald W. Schafer">Ronald W. Schafer</a>, Mark A. Yoder: <i>Signal Processing First</i>, Prentice Hall, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-13-090999-8" title="Special:BookSources/0-13-090999-8">0-13-090999-8</a></li> <li>Bernard Mulgrew, Peter Grant, John Thompson: <i>Digital Signal Processing – Concepts and Applications</i>, Palgrave Macmillan, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-333-96356-3" title="Special:BookSources/0-333-96356-3">0-333-96356-3</a></li> <li>Boaz Porat: <i>A Course in Digital Signal Processing</i>, Wiley, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-14961-6" title="Special:BookSources/0-471-14961-6">0-471-14961-6</a></li> <li>John G. Proakis, <a href="/wiki/Dimitris_Manolakis" title="Dimitris Manolakis">Dimitris Manolakis</a>: <i>Digital Signal Processing: Principles, Algorithms and Applications</i>, 4th ed, Pearson, April 2006, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0131873742" title="Special:BookSources/978-0131873742">978-0131873742</a></li> <li>John G. Proakis: <i>A Self-Study Guide for Digital Signal Processing</i>, Prentice Hall, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-13-143239-7" title="Special:BookSources/0-13-143239-7">0-13-143239-7</a></li> <li>Charles A. Schuler: <i>Digital Signal Processing: A Hands-On Approach</i>, McGraw-Hill, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-07-829744-3" title="Special:BookSources/0-07-829744-3">0-07-829744-3</a></li> <li>Doug Smith: <i>Digital Signal Processing Technology: Essentials of the Communications Revolution</i>, American Radio Relay League, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-87259-819-5" title="Special:BookSources/0-87259-819-5">0-87259-819-5</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmith2002" class="citation book cs1">Smith, Steven W. (2002). <a rel="nofollow" class="external text" href="http://www.dspguide.com"><i>Digital Signal Processing: A Practical Guide for Engineers and Scientists</i></a>. Newnes. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7506-7444-X" title="Special:BookSources/0-7506-7444-X"><bdi>0-7506-7444-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Digital+Signal+Processing%3A+A+Practical+Guide+for+Engineers+and+Scientists&rft.pub=Newnes&rft.date=2002&rft.isbn=0-7506-7444-X&rft.aulast=Smith&rft.aufirst=Steven+W.&rft_id=http%3A%2F%2Fwww.dspguide.com&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADigital+signal+processing" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStein2000" class="citation book cs1">Stein, Jonathan Yaakov (2000-10-09). <i>Digital Signal Processing, a Computer Science Perspective</i>. Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-29546-9" title="Special:BookSources/0-471-29546-9"><bdi>0-471-29546-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Digital+Signal+Processing%2C+a+Computer+Science+Perspective&rft.pub=Wiley&rft.date=2000-10-09&rft.isbn=0-471-29546-9&rft.aulast=Stein&rft.aufirst=Jonathan+Yaakov&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADigital+signal+processing" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStergiopoulos2000" class="citation book cs1">Stergiopoulos, Stergios (2000). <i>Advanced Signal Processing Handbook: Theory and Implementation for Radar, Sonar, and Medical Imaging Real-Time Systems</i>. CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8493-3691-0" title="Special:BookSources/0-8493-3691-0"><bdi>0-8493-3691-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Advanced+Signal+Processing+Handbook%3A+Theory+and+Implementation+for+Radar%2C+Sonar%2C+and+Medical+Imaging+Real-Time+Systems&rft.pub=CRC+Press&rft.date=2000&rft.isbn=0-8493-3691-0&rft.aulast=Stergiopoulos&rft.aufirst=Stergios&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADigital+signal+processing" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVan_De_Vegte2001" class="citation book cs1">Van De Vegte, Joyce (2001). <i>Fundamentals of Digital Signal Processing</i>. Prentice Hall. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-13-016077-6" title="Special:BookSources/0-13-016077-6"><bdi>0-13-016077-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fundamentals+of+Digital+Signal+Processing&rft.pub=Prentice+Hall&rft.date=2001&rft.isbn=0-13-016077-6&rft.aulast=Van+De+Vegte&rft.aufirst=Joyce&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADigital+signal+processing" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOppenheimSchafer2001" class="citation book cs1">Oppenheim, Alan V.; Schafer, Ronald W. (2001). <i>Discrete-Time Signal Processing</i>. Pearson. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-292-02572-7" title="Special:BookSources/1-292-02572-7"><bdi>1-292-02572-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Discrete-Time+Signal+Processing&rft.pub=Pearson&rft.date=2001&rft.isbn=1-292-02572-7&rft.aulast=Oppenheim&rft.aufirst=Alan+V.&rft.au=Schafer%2C+Ronald+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADigital+signal+processing" class="Z3988"></span></li> <li>Hayes, Monson H. Statistical digital signal processing and modeling. John Wiley & Sons, 2009. (with <a rel="nofollow" class="external text" href="https://www.mathworks.com/matlabcentral/fileexchange/2183-statistical-digital-signal-processing-and-modeling?s_tid=prof_contriblnk">MATLAB scripts</a>)</li></ul> </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=Digital_signal_processing&action=edit&section=41" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFB._SOMANATHAN_NAIR2002" class="citation book cs1">B. SOMANATHAN NAIR (2002). <i>Digital electronics and logic design</i>. PHI Learning Pvt. Ltd. p. 289. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9788120319561" title="Special:BookSources/9788120319561"><bdi>9788120319561</bdi></a>. <q>Digital signals are fixed-width pulses, which occupy only one of two levels of amplitude.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Digital+electronics+and+logic+design&rft.pages=289&rft.pub=PHI+Learning+Pvt.+Ltd.&rft.date=2002&rft.isbn=9788120319561&rft.au=B.+SOMANATHAN+NAIR&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADigital+signal+processing" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJoseph_Migga_Kizza2005" class="citation book cs1">Joseph Migga Kizza (2005). <i>Computer Network Security</i>. Springer Science & Business Media. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780387204734" title="Special:BookSources/9780387204734"><bdi>9780387204734</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Computer+Network+Security&rft.pub=Springer+Science+%26+Business+Media&rft.date=2005&rft.isbn=9780387204734&rft.au=Joseph+Migga+Kizza&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADigital+signal+processing" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=N6FDii6_nSEC&pg=PA151"><i>2000 Solved Problems in Digital Electronics</i></a>. <a href="/wiki/Tata_McGraw-Hill_Education" class="mw-redirect" title="Tata McGraw-Hill Education">Tata McGraw-Hill Education</a>. 2005. p. 151. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-058831-8" title="Special:BookSources/978-0-07-058831-8"><bdi>978-0-07-058831-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=2000+Solved+Problems+in+Digital+Electronics&rft.pages=151&rft.pub=Tata+McGraw-Hill+Education&rft.date=2005&rft.isbn=978-0-07-058831-8&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DN6FDii6_nSEC%26pg%3DPA151&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADigital+signal+processing" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBillings2013" class="citation book cs1">Billings, Stephen A. (Sep 2013). <i>Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains</i>. UK: Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-119-94359-4" title="Special:BookSources/978-1-119-94359-4"><bdi>978-1-119-94359-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Nonlinear+System+Identification%3A+NARMAX+Methods+in+the+Time%2C+Frequency%2C+and+Spatio-Temporal+Domains&rft.place=UK&rft.pub=Wiley&rft.date=2013-09&rft.isbn=978-1-119-94359-4&rft.aulast=Billings&rft.aufirst=Stephen+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADigital+signal+processing" 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="CITEREFBroeschStrannebyWalker2008" class="citation book cs1">Broesch, James D.; Stranneby, Dag; Walker, William (2008-10-20). <i>Digital Signal Processing: Instant access</i> (1 ed.). Butterworth-Heinemann-Newnes. p. 3. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780750689762" title="Special:BookSources/9780750689762"><bdi>9780750689762</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Digital+Signal+Processing%3A+Instant+access&rft.pages=3&rft.edition=1&rft.pub=Butterworth-Heinemann-Newnes&rft.date=2008-10-20&rft.isbn=9780750689762&rft.aulast=Broesch&rft.aufirst=James+D.&rft.au=Stranneby%2C+Dag&rft.au=Walker%2C+William&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADigital+signal+processing" class="Z3988"></span></span> </li> <li id="cite_note-Srivastava-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Srivastava_6-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSrivastavaSingh2013" class="citation book cs1">Srivastava, Viranjay M.; Singh, Ghanshyam (2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=fkO9BAAAQBAJ&pg=PA1"><i>MOSFET Technologies for Double-Pole Four-Throw Radio-Frequency Switch</i></a>. <a href="/wiki/Springer_Science_%26_Business_Media" class="mw-redirect" title="Springer Science & Business Media">Springer Science & Business Media</a>. p. 1. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9783319011653" title="Special:BookSources/9783319011653"><bdi>9783319011653</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=MOSFET+Technologies+for+Double-Pole+Four-Throw+Radio-Frequency+Switch&rft.pages=1&rft.pub=Springer+Science+%26+Business+Media&rft.date=2013&rft.isbn=9783319011653&rft.aulast=Srivastava&rft.aufirst=Viranjay+M.&rft.au=Singh%2C+Ghanshyam&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DfkO9BAAAQBAJ%26pg%3DPA1&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADigital+signal+processing" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWalden1999" class="citation journal cs1">Walden, R. 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Retrieved <span class="nowrap">2008-05-10</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=FPGA-Based+Image+Processing+Accelerator&rft.date=2006&rft.au=JPFix&rft_id=http%3A%2F%2Fwww.jpfix.com%2FAbout_Us%2FArticles%2FFPGA-Based_Image_Processing_Ac%2Ffpga-based_image_processing_ac.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADigital+signal+processing" class="Z3988"></span></span> </li> <li id="cite_note-:0-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-:0_21-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKapinchevBraduPodoleanu2019" class="citation book cs1">Kapinchev, Konstantin; Bradu, Adrian; Podoleanu, Adrian (December 2019). <a rel="nofollow" class="external text" href="https://ieeexplore.ieee.org/document/9008720">"Parallel Approaches to Digital Signal Processing Algorithms with Applications in Medical Imaging"</a>. <a rel="nofollow" class="external text" href="https://kar.kent.ac.uk/80930/1/Kapinchev2019.pdf"><i>2019 13th International Conference on Signal Processing and Communication Systems (ICSPCS)</i></a> <span class="cs1-format">(PDF)</span>. pp. 1–7. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FICSPCS47537.2019.9008720">10.1109/ICSPCS47537.2019.9008720</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-7281-2194-9" title="Special:BookSources/978-1-7281-2194-9"><bdi>978-1-7281-2194-9</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:211686462">211686462</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Parallel+Approaches+to+Digital+Signal+Processing+Algorithms+with+Applications+in+Medical+Imaging&rft.btitle=2019+13th+International+Conference+on+Signal+Processing+and+Communication+Systems+%28ICSPCS%29&rft.pages=1-7&rft.date=2019-12&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A211686462%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FICSPCS47537.2019.9008720&rft.isbn=978-1-7281-2194-9&rft.aulast=Kapinchev&rft.aufirst=Konstantin&rft.au=Bradu%2C+Adrian&rft.au=Podoleanu%2C+Adrian&rft_id=https%3A%2F%2Fieeexplore.ieee.org%2Fdocument%2F9008720&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADigital+signal+processing" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRabinerGold1975" class="citation book cs1"><a href="/wiki/Lawrence_Rabiner" title="Lawrence Rabiner">Rabiner, Lawrence R.</a>; Gold, Bernard (1975). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/theoryapplicatio00rabi"><i>Theory and application of digital signal processing</i></a></span>. Englewood Cliffs, NJ: Prentice-Hall, Inc. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0139141010" title="Special:BookSources/978-0139141010"><bdi>978-0139141010</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theory+and+application+of+digital+signal+processing&rft.place=Englewood+Cliffs%2C+NJ&rft.pub=Prentice-Hall%2C+Inc.&rft.date=1975&rft.isbn=978-0139141010&rft.aulast=Rabiner&rft.aufirst=Lawrence+R.&rft.au=Gold%2C+Bernard&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ftheoryapplicatio00rabi&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADigital+signal+processing" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKerckhoffListenbergerValente2008" class="citation journal cs1">Kerckhoff, Jessica; Listenberger, Jennifer; Valente, Michael (October 1, 2008). <a rel="nofollow" class="external text" href="https://digitalcommons.wustl.edu/audio_hapubs/28">"Advances in hearing aid technology"</a>. <i>Contemporary Issues in Communication Science and Disorders</i>. <b>35</b>: 102–112. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1044%2Fcicsd_35_F_102">10.1044/cicsd_35_F_102</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Contemporary+Issues+in+Communication+Science+and+Disorders&rft.atitle=Advances+in+hearing+aid+technology&rft.volume=35&rft.pages=102-112&rft.date=2008-10-01&rft_id=info%3Adoi%2F10.1044%2Fcicsd_35_F_102&rft.aulast=Kerckhoff&rft.aufirst=Jessica&rft.au=Listenberger%2C+Jennifer&rft.au=Valente%2C+Michael&rft_id=https%3A%2F%2Fdigitalcommons.wustl.edu%2Faudio_hapubs%2F28&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADigital+signal+processing" class="Z3988"></span></span> </li> </ol></div></div> <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 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href="/wiki/Template:Digital_electronics" title="Template:Digital electronics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Digital_electronics" title="Template talk:Digital electronics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Digital_electronics" title="Special:EditPage/Template:Digital electronics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Digital_electronics" style="font-size:114%;margin:0 4em"><a href="/wiki/Digital_electronics" title="Digital electronics">Digital electronics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Electronic_component" title="Electronic component">Components</a></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/Transistor" title="Transistor">Transistor</a></li> <li><a href="/wiki/Resistor" title="Resistor">Resistor</a></li> <li><a href="/wiki/Inductor" title="Inductor">Inductor</a></li> <li><a href="/wiki/Capacitor" title="Capacitor">Capacitor</a></li> <li><a href="/wiki/Printed_electronics" title="Printed electronics">Printed electronics</a></li> <li><a href="/wiki/Printed_circuit_board" title="Printed circuit board">Printed circuit board</a></li> <li><a href="/wiki/Electronic_circuit" title="Electronic circuit">Electronic circuit</a></li> <li><a href="/wiki/Flip-flop_(electronics)" title="Flip-flop (electronics)">Flip-flop</a></li> <li><a href="/wiki/Memory_cell_(computing)" title="Memory cell (computing)">Memory cell</a></li> <li><a href="/wiki/Combinational_logic" title="Combinational logic">Combinational logic</a></li> <li><a href="/wiki/Sequential_logic" title="Sequential logic">Sequential logic</a></li> <li><a href="/wiki/Logic_gate" title="Logic gate">Logic gate</a></li> <li><a href="/wiki/Boolean_circuit" title="Boolean circuit">Boolean circuit</a></li> <li><a href="/wiki/Integrated_circuit" title="Integrated circuit">Integrated circuit</a> (IC)</li> <li><a href="/wiki/Hybrid_integrated_circuit" title="Hybrid integrated circuit">Hybrid integrated circuit</a> (HIC)</li> <li><a href="/wiki/Mixed-signal_integrated_circuit" title="Mixed-signal integrated circuit">Mixed-signal integrated circuit</a></li> <li><a href="/wiki/Three-dimensional_integrated_circuit" title="Three-dimensional integrated circuit">Three-dimensional integrated circuit</a> (3D IC)</li> <li><a href="/wiki/Emitter-coupled_logic" title="Emitter-coupled logic">Emitter-coupled logic</a> (ECL)</li> <li><a href="/wiki/Erasable_programmable_logic_device" class="mw-redirect" title="Erasable programmable logic device">Erasable programmable logic device</a> (EPLD)</li> <li><a href="/wiki/Macrocell_array" title="Macrocell array">Macrocell array</a></li> <li><a href="/wiki/Programmable_logic_array" title="Programmable logic array">Programmable logic array</a> (PLA)</li> <li><a href="/wiki/Programmable_logic_device" title="Programmable logic device">Programmable logic device</a> (PLD)</li> <li><a href="/wiki/Programmable_Array_Logic" title="Programmable Array Logic">Programmable Array Logic</a> (PAL)</li> <li><a href="/wiki/Generic_Array_Logic" title="Generic Array Logic">Generic Array Logic</a> (GAL)</li> <li><a href="/wiki/Complex_programmable_logic_device" title="Complex programmable logic device">Complex programmable logic device</a> (CPLD)</li> <li><a href="/wiki/Field-programmable_gate_array" title="Field-programmable gate array">Field-programmable gate array</a> (FPGA)</li> <li><a href="/wiki/Field-programmable_object_array" title="Field-programmable object array">Field-programmable object array</a> (FPOA)</li> <li><a href="/wiki/Application-specific_integrated_circuit" title="Application-specific integrated circuit">Application-specific integrated circuit</a> (ASIC)</li> <li><a href="/wiki/Tensor_Processing_Unit" title="Tensor Processing Unit">Tensor Processing Unit</a> (TPU)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;">Theory</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/Digital_signal" title="Digital signal">Digital signal</a></li> <li><a href="/wiki/Boolean_algebra" title="Boolean algebra">Boolean algebra</a></li> <li><a href="/wiki/Logic_synthesis" title="Logic synthesis">Logic synthesis</a></li> <li><a href="/wiki/Logic_in_computer_science" title="Logic in computer science">Logic in computer science</a></li> <li><a href="/wiki/Computer_architecture" title="Computer architecture">Computer architecture</a></li> <li><a href="/wiki/Digital_signal_(signal_processing)" title="Digital signal (signal processing)">Digital signal</a> <ul><li><a class="mw-selflink selflink">Digital signal processing</a></li></ul></li> <li><a href="/wiki/Circuit_minimization_for_Boolean_functions" class="mw-redirect" title="Circuit minimization for Boolean functions">Circuit minimization</a></li> <li><a href="/wiki/Switching_circuit_theory" title="Switching circuit theory">Switching circuit theory</a></li> <li><a href="/wiki/Gate_equivalent" title="Gate equivalent">Gate equivalent</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="/wiki/Electronics_design" class="mw-redirect" title="Electronics design">Design</a></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/Logic_synthesis" title="Logic synthesis">Logic synthesis</a></li> <li><a href="/wiki/Place_and_route" title="Place and route">Place and route</a> <ul><li><a href="/wiki/Placement_(electronic_design_automation)" title="Placement (electronic design automation)">Placement</a></li> <li><a href="/wiki/Routing_(electronic_design_automation)" title="Routing (electronic design automation)">Routing</a></li></ul></li> <li><a href="/wiki/Transaction-level_modeling" title="Transaction-level modeling">Transaction-level modeling</a></li> <li><a href="/wiki/Register-transfer_level" title="Register-transfer level">Register-transfer level</a> <ul><li><a href="/wiki/Hardware_description_language" title="Hardware description language">Hardware description language</a></li> <li><a href="/wiki/High-level_synthesis" title="High-level synthesis">High-level synthesis</a></li></ul></li> <li><a href="/wiki/Formal_equivalence_checking" title="Formal equivalence checking">Formal equivalence checking</a></li> <li><a href="/wiki/Synchronous_circuit" title="Synchronous circuit">Synchronous logic</a></li> <li><a href="/wiki/Asynchronous_circuit" title="Asynchronous circuit">Asynchronous logic</a></li> <li><a href="/wiki/Finite-state_machine" title="Finite-state machine">Finite-state machine</a> <ul><li><a href="/wiki/Hierarchical_state_machine" class="mw-redirect" title="Hierarchical state machine">Hierarchical state machine</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;">Applications</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/Computer_hardware" title="Computer hardware">Computer hardware</a> <ul><li><a href="/wiki/Hardware_acceleration" title="Hardware acceleration">Hardware acceleration</a></li></ul></li> <li><a href="/wiki/Digital_audio" title="Digital audio">Digital audio</a> <ul><li><a href="/wiki/Digital_radio" title="Digital radio">radio</a></li></ul></li> <li><a href="/wiki/Digital_photography" title="Digital photography">Digital photography</a></li> <li><a href="/wiki/Telephony#Digital_telephony" title="Telephony">Digital 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href="/wiki/Special:EditPage/Template:Digital_signal_processing" title="Special:EditPage/Template:Digital signal processing"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Digital_signal_processing" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">Digital signal processing</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theory</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Detection_theory" title="Detection theory">Detection theory</a></li> <li><a href="/wiki/Discrete_time_and_continuous_time" title="Discrete time and continuous time">Discrete signal</a></li> <li><a href="/wiki/Estimation_theory" title="Estimation theory">Estimation theory</a></li> <li><a href="/wiki/Nyquist%E2%80%93Shannon_sampling_theorem" title="Nyquist–Shannon sampling theorem">Nyquist–Shannon sampling theorem</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Sub-fields</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Audio_signal_processing" title="Audio signal processing">Audio signal processing</a></li> <li><a href="/wiki/Digital_image_processing" title="Digital image processing">Digital image processing</a></li> <li><a href="/wiki/Speech_processing" title="Speech processing">Speech processing</a></li> <li><a href="/wiki/Statistical_signal_processing" class="mw-redirect" title="Statistical signal processing">Statistical signal processing</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Techniques</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Z-transform" title="Z-transform">Z-transform</a> <ul><li><a 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