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[r]" accesskey="r"><span>Perubahan terbaru</span></a></li><li id="n-Artikel-pilihan" class="mw-list-item"><a href="/wiki/Wikipedia:Artikel_pilihan/Topik"><span>Artikel pilihan</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Peristiwa_terkini" title="Temukan informasi tentang peristiwa terkini"><span>Peristiwa terkini</span></a></li><li id="n-newpage" class="mw-list-item"><a href="/wiki/Istimewa:Halaman_baru"><span>Halaman baru</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Istimewa:Halaman_sembarang" title="Tampilkan sembarang halaman [x]" accesskey="x"><span>Halaman sembarang</span></a></li><li id="n-specialpages" class="mw-list-item"><a href="/wiki/Istimewa:Halaman_istimewa"><span>Halaman istimewa</span></a></li> </ul> </div> </div> <div id="p-Komunitas" class="vector-menu mw-portlet mw-portlet-Komunitas" > <div class="vector-menu-heading"> Komunitas </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-Warung-Kopi" class="mw-list-item"><a href="/wiki/Wikipedia:Warung_Kopi"><span>Warung Kopi</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Portal:Komunitas" title="Tentang proyek, apa yang dapat Anda lakukan, di mana untuk mencari sesuatu"><span>Portal komunitas</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Bantuan:Isi" title="Tempat mencari bantuan."><span>Bantuan</span></a></li> </ul> </div> </div> <div id="p-Wikipedia" class="vector-menu mw-portlet mw-portlet-Wikipedia" > <div class="vector-menu-heading"> Wikipedia </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:Perihal"><span>Tentang Wikipedia</span></a></li><li id="n-Pancapilar" class="mw-list-item"><a href="/wiki/Wikipedia:Pancapilar"><span>Pancapilar</span></a></li><li id="n-Kebijakan" class="mw-list-item"><a href="/wiki/Wikipedia:Kebijakan_dan_pedoman"><span>Kebijakan</span></a></li><li id="n-Hubungi-kami" class="mw-list-item"><a href="/wiki/Wikipedia:Hubungi_kami"><span>Hubungi kami</span></a></li><li id="n-Bak-pasir" class="mw-list-item"><a href="/wiki/Wikipedia:Bak_pasir"><span>Bak pasir</span></a></li> </ul> </div> </div> <div id="p-Bagikan" class="vector-menu mw-portlet mw-portlet-Bagikan emptyPortlet" > <div class="vector-menu-heading"> Bagikan </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Halaman_Utama" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="Ensiklopedia Bebas" src="/static/images/mobile/copyright/wikipedia-tagline-id.svg" width="120" height="14" style="width: 7.5em; height: 0.875em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Istimewa:Pencarian" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Cari di Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Pencarian</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Telusuri Wikipedia" aria-label="Telusuri Wikipedia" autocapitalize="sentences" title="Cari di Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Istimewa:Pencarian"> </div> <button class="cdx-button cdx-search-input__end-button">Cari</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Perkakas pribadi"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Tampilan"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Tampilan" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Tampilan</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=id.wikipedia.org&uselang=id" class=""><span>Menyumbang</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Istimewa:Buat_akun&returnto=Wavelet" title="Anda dianjurkan untuk membuat akun dan masuk log; meskipun, hal itu tidak diwajibkan" class=""><span>Buat akun baru</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Istimewa:Masuk_log&returnto=Wavelet" title="Anda disarankan untuk masuk log, meskipun hal itu tidak diwajibkan. [o]" accesskey="o" class=""><span>Masuk log</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Opsi lainnya" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Perkakas pribadi" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Perkakas pribadi</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Menu pengguna" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=id.wikipedia.org&uselang=id"><span>Menyumbang</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Istimewa:Buat_akun&returnto=Wavelet" title="Anda dianjurkan untuk membuat akun dan masuk log; meskipun, hal itu tidak diwajibkan"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Buat akun baru</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Istimewa:Masuk_log&returnto=Wavelet" title="Anda disarankan untuk masuk log, meskipun hal itu tidak diwajibkan. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Masuk log</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Halaman penyunting yang telah keluar log <a href="/wiki/Bantuan:Pengantar" aria-label="Pelajari lebih lanjut tentang menyunting"><span>pelajari lebih lanjut</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Istimewa:Kontribusi_saya" title="Daftar suntingan yang dibuat dari alamat IP ini [y]" accesskey="y"><span>Kontribusi</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Istimewa:Pembicaraan_saya" title="Pembicaraan tentang suntingan dari alamat IP ini [n]" accesskey="n"><span>Pembicaraan</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Situs"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Daftar isi" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Daftar isi</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">pindah ke bilah sisi</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">sembunyikan</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Awal</div> </a> </li> <li id="toc-Transformasi_Wavelet" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Transformasi_Wavelet"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Transformasi Wavelet</span> </div> </a> <button aria-controls="toc-Transformasi_Wavelet-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>Gulingkan subbagian Transformasi Wavelet</span> </button> <ul id="toc-Transformasi_Wavelet-sublist" class="vector-toc-list"> <li id="toc-Perbandingan_dengan_Transformasi_Fourier" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Perbandingan_dengan_Transformasi_Fourier"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Perbandingan dengan Transformasi Fourier</span> </div> </a> <ul id="toc-Perbandingan_dengan_Transformasi_Fourier-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Transformasi_Wavelet_Kontinu" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Transformasi_Wavelet_Kontinu"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Transformasi Wavelet Kontinu</span> </div> </a> <ul id="toc-Transformasi_Wavelet_Kontinu-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Transformasi_Wavelet_Diskrit" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Transformasi_Wavelet_Diskrit"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Transformasi Wavelet Diskrit</span> </div> </a> <ul id="toc-Transformasi_Wavelet_Diskrit-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Aplikasi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Aplikasi"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Aplikasi</span> </div> </a> <button aria-controls="toc-Aplikasi-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>Gulingkan subbagian Aplikasi</span> </button> <ul id="toc-Aplikasi-sublist" class="vector-toc-list"> <li id="toc-TWK" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#TWK"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>TWK</span> </div> </a> <ul id="toc-TWK-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-TWD" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#TWD"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>TWD</span> </div> </a> <ul id="toc-TWD-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Lihat_pula" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Lihat_pula"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Lihat pula</span> </div> </a> <ul id="toc-Lihat_pula-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Referensi" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Referensi"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Referensi</span> </div> </a> <ul id="toc-Referensi-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pranala_luar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Pranala_luar"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Pranala luar</span> </div> </a> <ul id="toc-Pranala_luar-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="Daftar isi" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Daftar Isi" > <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="Gulingkan daftar isi" > <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">Gulingkan daftar isi</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">Wavelet</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="Pergi ke artikel dalam bahasa lain. Terdapat 26 bahasa" > <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-26" 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">26 bahasa</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%D9%88%D9%8A%D8%AC%D8%A9_(%D8%AF%D8%A7%D9%84%D8%A9)" title="مويجة (دالة) – Arab" lang="ar" hreflang="ar" data-title="مويجة (دالة)" data-language-autonym="العربية" data-language-local-name="Arab" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Veyvlet" title="Veyvlet – Azerbaijani" lang="az" hreflang="az" data-title="Veyvlet" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%92%D0%B5%D0%B9%D0%B2%D0%BB%D0%B5%D1%82" title="Вейвлет – Belarusia" lang="be" hreflang="be" data-title="Вейвлет" data-language-autonym="Беларуская" data-language-local-name="Belarusia" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A3%D0%B5%D0%B9%D0%B2%D0%BB%D0%B5%D1%82" title="Уейвлет – Bulgaria" lang="bg" hreflang="bg" data-title="Уейвлет" data-language-autonym="Български" data-language-local-name="Bulgaria" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Ondeta" title="Ondeta – Katalan" lang="ca" hreflang="ca" data-title="Ondeta" data-language-autonym="Català" data-language-local-name="Katalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Vlnka" title="Vlnka – Ceko" lang="cs" hreflang="cs" data-title="Vlnka" data-language-autonym="Čeština" data-language-local-name="Ceko" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Wavelet" title="Wavelet – Jerman" lang="de" hreflang="de" data-title="Wavelet" data-language-autonym="Deutsch" data-language-local-name="Jerman" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Wavelet" title="Wavelet – Inggris" lang="en" hreflang="en" data-title="Wavelet" data-language-autonym="English" data-language-local-name="Inggris" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Ondosimila%C4%B5o" title="Ondosimilaĵo – Esperanto" lang="eo" hreflang="eo" data-title="Ondosimilaĵo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Ond%C3%ADcula" title="Ondícula – Spanyol" lang="es" hreflang="es" data-title="Ondícula" data-language-autonym="Español" data-language-local-name="Spanyol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Lainik" title="Lainik – Estonia" lang="et" hreflang="et" data-title="Lainik" data-language-autonym="Eesti" data-language-local-name="Estonia" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D9%88%D8%AC%DA%A9" title="موجک – Persia" lang="fa" hreflang="fa" data-title="موجک" data-language-autonym="فارسی" data-language-local-name="Persia" 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/Ondelette" title="Ondelette – Prancis" lang="fr" hreflang="fr" data-title="Ondelette" data-language-autonym="Français" data-language-local-name="Prancis" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Ondl%C3%A8t" title="Ondlèt – Kreol Haiti" lang="ht" hreflang="ht" data-title="Ondlèt" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Kreol Haiti" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Wavelet" title="Wavelet – Italia" lang="it" hreflang="it" data-title="Wavelet" data-language-autonym="Italiano" data-language-local-name="Italia" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A6%E3%82%A7%E3%83%BC%E3%83%96%E3%83%AC%E3%83%83%E3%83%88" title="ウェーブレット – Jepang" lang="ja" hreflang="ja" data-title="ウェーブレット" data-language-autonym="日本語" data-language-local-name="Jepang" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9B%A8%EC%9D%B4%EB%B8%94%EB%A6%BF" title="웨이블릿 – Korea" lang="ko" hreflang="ko" data-title="웨이블릿" data-language-autonym="한국어" data-language-local-name="Korea" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Vilnel%C4%97_(matematika)" title="Vilnelė (matematika) – Lituania" lang="lt" hreflang="lt" data-title="Vilnelė (matematika)" data-language-autonym="Lietuvių" data-language-local-name="Lituania" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Wavelet" title="Wavelet – Belanda" lang="nl" hreflang="nl" data-title="Wavelet" data-language-autonym="Nederlands" data-language-local-name="Belanda" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Falki" title="Falki – Polski" lang="pl" hreflang="pl" data-title="Falki" data-language-autonym="Polski" data-language-local-name="Polski" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Wavelet" title="Wavelet – Portugis" lang="pt" hreflang="pt" data-title="Wavelet" data-language-autonym="Português" data-language-local-name="Portugis" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%92%D0%B5%D0%B9%D0%B2%D0%BB%D0%B5%D1%82" title="Вейвлет – Rusia" lang="ru" hreflang="ru" data-title="Вейвлет" data-language-autonym="Русский" data-language-local-name="Rusia" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Wavelet" title="Wavelet – Simple English" lang="en-simple" hreflang="en-simple" data-title="Wavelet" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Wavelet" title="Wavelet – Swedia" lang="sv" hreflang="sv" data-title="Wavelet" data-language-autonym="Svenska" data-language-local-name="Swedia" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%92%D0%B5%D0%B9%D0%B2%D0%BB%D0%B5%D1%82" title="Вейвлет – Ukraina" lang="uk" hreflang="uk" data-title="Вейвлет" data-language-autonym="Українська" data-language-local-name="Ukraina" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%B0%8F%E6%B3%A2%E5%88%86%E6%9E%90" title="小波分析 – Tionghoa" lang="zh" hreflang="zh" data-title="小波分析" data-language-autonym="中文" data-language-local-name="Tionghoa" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q831390#sitelinks-wikipedia" title="Sunting pranala interwiki" class="wbc-editpage">Sunting pranala</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Ruang nama"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Wavelet" title="Lihat halaman isi [c]" accesskey="c"><span>Halaman</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Pembicaraan:Wavelet" rel="discussion" title="Pembicaraan halaman isi [t]" accesskey="t"><span>Pembicaraan</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Ubah varian bahasa" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Bahasa Indonesia</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Tampilan"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Wavelet"><span>Baca</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Wavelet&veaction=edit" title="Sunting halaman ini [v]" accesskey="v"><span>Sunting</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Wavelet&action=edit" title="Sunting kode sumber halaman ini [e]" accesskey="e"><span>Sunting sumber</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Wavelet&action=history" title="Revisi sebelumnya dari halaman ini. [h]" accesskey="h"><span>Lihat riwayat</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Peralatan halaman"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Perkakas" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Perkakas</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Perkakas</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">pindah ke bilah sisi</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">sembunyikan</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Opsi lainnya" > <div class="vector-menu-heading"> Tindakan </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Wavelet"><span>Baca</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Wavelet&veaction=edit" title="Sunting halaman ini [v]" accesskey="v"><span>Sunting</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Wavelet&action=edit" title="Sunting kode sumber halaman ini [e]" accesskey="e"><span>Sunting sumber</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Wavelet&action=history"><span>Lihat riwayat</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Umum </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Istimewa:Pranala_balik/Wavelet" title="Daftar semua halaman wiki yang memiliki pranala ke halaman ini [j]" accesskey="j"><span>Pranala balik</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Istimewa:Perubahan_terkait/Wavelet" rel="nofollow" title="Perubahan terbaru halaman-halaman yang memiliki pranala ke halaman ini [k]" accesskey="k"><span>Perubahan terkait</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Wavelet&oldid=26510878" title="Pranala permanen untuk revisi halaman ini"><span>Pranala permanen</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Wavelet&action=info" title="Informasi lanjut tentang halaman ini"><span>Informasi halaman</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Istimewa:Kutip&page=Wavelet&id=26510878&wpFormIdentifier=titleform" title="Informasi tentang bagaimana mengutip halaman ini"><span>Kutip halaman ini</span></a></li><li id="t-urlshortener" class="mw-list-item"><a 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.mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}html.client-js body.skin-minerva .mw-parser-output .mbox-text-span{margin-left:23px!important}@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-Tanpa_referensi 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/Berkas:Question_book-new.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/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/commons/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/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">Artikel ini <b>tidak memiliki <a href="/wiki/Wikipedia:Kutip_sumber_tulisan" title="Wikipedia:Kutip sumber tulisan">referensi</a> atau <a href="/wiki/Wikipedia:Sumber_tepercaya" title="Wikipedia:Sumber tepercaya">sumber tepercaya</a></b> sehingga isinya tidak bisa <a href="/wiki/Wikipedia:Pemastian" title="Wikipedia:Pemastian">dipastikan</a>.<span class="hide-when-compact"> Tolong bantu <span class="plainlinks"><a class="external text" href="https://id.wikipedia.org/w/index.php?title=Wavelet&action=edit">perbaiki artikel ini</a></span> dengan menambahkan referensi yang layak. Tulisan tanpa sumber dapat dipertanyakan dan dihapus sewaktu-waktu.<br /><small><span class="plainlinks"><i>Cari sumber:</i> <a rel="nofollow" class="external text" href="//google.com/search?as_eq=wikipedia&q=%22Wavelet%22&num=50">"Wavelet"</a> – <a rel="nofollow" class="external text" href="//google.com/search?q=%22Wavelet%22&tbm=nws">berita</a> <b>·</b> <a rel="nofollow" class="external text" href="//google.com/search?&q=%22Wavelet%22+site:news.google.com/newspapers&source=newspapers">surat kabar</a> <b>·</b> <a rel="nofollow" class="external text" href="//google.com/search?tbs=bks:1&q=%22Wavelet%22">buku</a> <b>·</b> <a rel="nofollow" class="external text" href="//scholar.google.com/scholar?q=%22Wavelet%22">cendekiawan</a> <b>·</b> <a rel="nofollow" class="external text" href="http://www.jstor.org/action/doBasicSearch?Query=%22Wavelet%22&acc=on&wc=on">JSTOR</a></span></small></span></div></td></tr></tbody></table> <p>Teori <b>wavelet</b> adalah suatu konsep relatif baru yang dikembangkan. Kata “<i>Wavelet</i>” sendiri diberikan oleh <a href="/w/index.php?title=Jean_Morlet&action=edit&redlink=1" class="new" title="Jean Morlet (halaman belum tersedia)">Jean Morlet</a> dan <a href="/w/index.php?title=Alex_Grossmann&action=edit&redlink=1" class="new" title="Alex Grossmann (halaman belum tersedia)">Alex Grossmann</a> pada awal tahun <a href="/wiki/1980" title="1980">1980</a>-an, dan kata ini berasal dari <a href="/wiki/Bahasa_Prancis" title="Bahasa Prancis">bahasa Prancis</a>, “<i>ondelette</i>” yang berarti gelombang kecil. Kata “<i>onde</i>” yang berarti gelombang kemudian diterjemahkan ke <a href="/wiki/Bahasa_Inggris" title="Bahasa Inggris">bahasa Inggris</a> menjadi “<i>wave</i>”, lalu digabung dengan kata aslinya sehingga terbentuk kata baru “<i>wavelet</i>”. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Transformasi_Wavelet">Transformasi Wavelet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wavelet&veaction=edit&section=1" title="Sunting bagian: Transformasi Wavelet" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Wavelet&action=edit&section=1" title="Sunting kode sumber bagian: Transformasi Wavelet"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Transformasi wavelet dibagi menjadi dua, yaitu transformasi wavelet kontinu (TWK) dan transformasi wavelet diskrit (TWD). </p> <div class="mw-heading mw-heading3"><h3 id="Perbandingan_dengan_Transformasi_Fourier">Perbandingan dengan Transformasi Fourier</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wavelet&veaction=edit&section=2" title="Sunting bagian: Perbandingan dengan Transformasi Fourier" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Wavelet&action=edit&section=2" title="Sunting kode sumber bagian: Perbandingan dengan Transformasi Fourier"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sampai sekarang <a href="/wiki/Transformasi_Fourier" title="Transformasi Fourier">transformasi Fourier</a> mungkin masih menjadi transformasi yang paling populer di area <a href="/wiki/Pemrosesan_sinyal_digital" class="mw-redirect" title="Pemrosesan sinyal digital">pemrosesan sinyal digital</a> (PSD). Transformasi Fourier memberitahu kita informasi <a href="/wiki/Frekuensi" title="Frekuensi">frekuensi</a> dari sebuah <a href="/wiki/Sinyal" class="mw-redirect" title="Sinyal">sinyal</a>, tapi tidak informasi waktu (kita tidak tahu di mana frekuensi itu terjadi). </p><p>Karena itulah transformasi Fourier hanya cocok untuk sinyal <a href="/w/index.php?title=Stationari&action=edit&redlink=1" class="new" title="Stationari (halaman belum tersedia)">stationari</a> (sinyal yang informasi frekuensinya tidak berubah menurut waktu). Untuk menganalisis sinyal yang frekuensinya bervariasi di dalam waktu, diperlukan suatu transformasi yang dapat memberikan resolusi frekuensi dan waktu disaat yang bersamaan, biasa disebut <a href="/w/index.php?title=Analisis_multi_resolusi&action=edit&redlink=1" class="new" title="Analisis multi resolusi (halaman belum tersedia)">analisis multi resolusi</a> (AMR). AMR dirancang untuk memberikan resolusi waktu yang baik dan resolusi frekuensi yang buruk pada frekuensi tinggi suatu sinyal, serta resolusi frekuensi yang baik dan resolusi waktu yang buruk pada frekuensi rendah suatu sinyal. Pendekatan ini sangat berguna untuk menganalisis sinyal dalam aplikasi-aplikasi praktis yang memang memiliki lebih banyak frekuensi rendah. </p><p>Transformasi wavelet adalah suatu AMR yang dapat merepresentasikan informasi waktu dan frekuensi suatu sinyal dengan baik. Transformasi wavelet menggunakan sebuah jendela modulasi yang fleksibel, ini yang paling membedakannya dengan <a href="/w/index.php?title=Transformasi_Fourier_waktu-singkat&action=edit&redlink=1" class="new" title="Transformasi Fourier waktu-singkat (halaman belum tersedia)">transformasi Fourier waktu-singkat</a> (STFT), yang merupakan pengembangan dari transformasi Fourier. STFT menggunakan jendela <a href="/wiki/Modulasi" title="Modulasi">modulasi</a> yang besarnya tetap, ini menyebabkan dilema karena jendela yang sempit akan memberikan resolusi frekuensi yang buruk dan sebaliknya jendela yang lebar akan menyebabkan resolusi waktu yang buruk. </p> <div class="mw-heading mw-heading3"><h3 id="Transformasi_Wavelet_Kontinu">Transformasi Wavelet Kontinu</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wavelet&veaction=edit&section=3" title="Sunting bagian: Transformasi Wavelet Kontinu" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Wavelet&action=edit&section=3" title="Sunting kode sumber bagian: Transformasi Wavelet Kontinu"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Cara kerja transformasi wavelet kontinu (TWK) adalah dengan menghitung <a href="/wiki/Konvolusi" title="Konvolusi">konvolusi</a> sebuah sinyal dengan sebuah jendela modulasi pada setiap waktu dengan setiap skala yang diinginkan. Jendela modulasi yang mempunyai skala fleksibel inilah yang biasa disebut induk wavelet atau fungsi dasar wavelet. </p><p>Dalam transformasi wavelet digunakan istilah <a href="/wiki/Translasi" class="mw-redirect mw-disambig" title="Translasi">translasi</a> dan <a href="/wiki/Skala" class="mw-redirect" title="Skala">skala</a>, karena istilah waktu dan frekuensi sudah digunakan oleh transformasi Fourier. Translasi adalah lokasi jendela modulasi saat digeser sepanjang sinyal, berhubungan dengan informasi waktu. Skala berhubungan dengan frekuensi, skala tinggi (frekuensi rendah) berhubungan dengan informasi global dari sebuah sinyal, sedangkan skala rendah (frekuensi tinggi) berhubungan dengan informasi detail. </p><p>TWK secara matematika dapat didefinisikan sebagai berikut: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma (s,\tau )=\int f(t)\psi _{s,\tau }^{*}(t)dt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mo stretchy="false">(</mo> <mi>s</mi> <mo>,</mo> <mi>τ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>∫</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <msubsup> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo>,</mo> <mi>τ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma (s,\tau )=\int f(t)\psi _{s,\tau }^{*}(t)dt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbe6da777139ce4675125dd4a3145eac06b9327c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:24.533ex; height:5.676ex;" alt="{\displaystyle \gamma (s,\tau )=\int f(t)\psi _{s,\tau }^{*}(t)dt}" /></span></dd></dl> <p>Pada rumus di atas, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \gamma (s,\tau )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>γ</mi> <mo stretchy="false">(</mo> <mi>s</mi> <mo>,</mo> <mi>τ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \gamma (s,\tau )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e1599fd523599a53df0e0c3216151851d1b0683" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.398ex; height:2.843ex;" alt="{\displaystyle \gamma (s,\tau )}" /></span> menyatakan fungsi sinyal setelah transformasi, dengan variabel s (skala) dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38a7dcde9730ef0853809fefc18d88771f95206c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.202ex; height:1.676ex;" alt="{\displaystyle \tau }" /></span> (translasi) sebagai dimensi baru. Fungsi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bf044fe2fbfc4bd8d6d7230f4108430263f9fd6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.927ex; height:2.843ex;" alt="{\displaystyle f(t)}" /></span> menyatakan sinyal asli sebelum transformasi. Fungsi dasar <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi _{s,\tau }^{*}(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo>,</mo> <mi>τ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi _{s,\tau }^{*}(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f1815f778f646c408ae523fca000facdd7bfea8f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:6.473ex; height:3.009ex;" alt="{\displaystyle \psi _{s,\tau }^{*}(t)}" /></span> disebut sebagai wavelet, dengan * menunjukkan konjugasi kompleks. </p><p>Dan inversi dari TWK secara matematika dapat didefinisikan sebagai berikut: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(t)=\int \int \gamma (s,\tau )\psi _{s,\tau }(t)d\tau ds}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>∫</mo> <mo>∫</mo> <mi>γ</mi> <mo stretchy="false">(</mo> <mi>s</mi> <mo>,</mo> <mi>τ</mi> <mo stretchy="false">)</mo> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo>,</mo> <mi>τ</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>τ</mi> <mi>d</mi> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(t)=\int \int \gamma (s,\tau )\psi _{s,\tau }(t)d\tau ds}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3dc3a7df970f4f4f50075a735f3d8d8ce394579" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:29.782ex; height:5.676ex;" alt="{\displaystyle f(t)=\int \int \gamma (s,\tau )\psi _{s,\tau }(t)d\tau ds}" /></span></dd></dl> <p>Seperti telah dibicarakan sebelumnya, fungsi dasar wavelet <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi _{s,\tau }(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo>,</mo> <mi>τ</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi _{s,\tau }(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/28f8689201b2fd05faf60b5e2e1ea1dbbfc06a99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:6.473ex; height:3.009ex;" alt="{\displaystyle \psi _{s,\tau }(t)}" /></span> dapat didesain sesuai kebutuhan untuk mendapatkan hasil transformasi yang terbaik, ini perbedaan mendasar dengan transformasi Fourier yang hanya menggunakan fungsi <a href="/wiki/Sinus" class="mw-redirect mw-disambig" title="Sinus">sinus</a> sebagai jendela modulasi. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Berkas:Wavelet_-_Mex_Hat.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Wavelet_-_Mex_Hat.png/220px-Wavelet_-_Mex_Hat.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/01/Wavelet_-_Mex_Hat.png/330px-Wavelet_-_Mex_Hat.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/01/Wavelet_-_Mex_Hat.png/440px-Wavelet_-_Mex_Hat.png 2x" data-file-width="560" data-file-height="420" /></a><figcaption>Wavelet Mexican Hat</figcaption></figure> <p>Fungsi dasar wavelet secara matematika dapat didefinisikan sebagai berikut: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi _{s,\tau }(t)={\frac {1}{\sqrt {s}}}\psi \left({\frac {t-\tau }{s}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo>,</mo> <mi>τ</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mi>s</mi> </msqrt> </mfrac> </mrow> <mi>ψ</mi> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>t</mi> <mo>−</mo> <mi>τ</mi> </mrow> <mi>s</mi> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi _{s,\tau }(t)={\frac {1}{\sqrt {s}}}\psi \left({\frac {t-\tau }{s}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e216af0ba134ff93f9227e2a9c8757e2640d360" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:24.473ex; height:6.509ex;" alt="{\displaystyle \psi _{s,\tau }(t)={\frac {1}{\sqrt {s}}}\psi \left({\frac {t-\tau }{s}}\right)}" /></span></dd></dl> <p>faktor <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{\sqrt {s}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mi>s</mi> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{\sqrt {s}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6668abc67b883e82b7f0af1225f559dd86ed36f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:3.862ex; height:6.176ex;" alt="{\displaystyle {\frac {1}{\sqrt {s}}}}" /></span> digunakan untuk <a href="/w/index.php?title=Normalisasi&action=edit&redlink=1" class="new" title="Normalisasi (halaman belum tersedia)">normalisasi</a> <a href="/wiki/Energi" title="Energi">energi</a> pada skala yang berubah-ubah. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Berkas:Wavelet_-_Morlet.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Wavelet_-_Morlet.png/220px-Wavelet_-_Morlet.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Wavelet_-_Morlet.png/330px-Wavelet_-_Morlet.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/Wavelet_-_Morlet.png/440px-Wavelet_-_Morlet.png 2x" data-file-width="560" data-file-height="420" /></a><figcaption>Wavelet Morlet</figcaption></figure> <p><a href="/w/index.php?title=Mexican_Hat&action=edit&redlink=1" class="new" title="Mexican Hat (halaman belum tersedia)">Mexican Hat</a>, yang merupakan normalisasi dari <a href="/wiki/Derivatif" title="Derivatif">derivatif</a> kedua fungsi <a href="/wiki/Gaussian" class="mw-redirect" title="Gaussian">Gaussian</a> adalah salah satu contoh fungsi dasar TWK: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi (t)={1 \over {{\sqrt {2\pi }}\sigma ^{3}}}\left(1-{t^{2} \over \sigma ^{2}}\right)e^{-t^{2} \over 2\sigma ^{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> <mi>π</mi> </msqrt> </mrow> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>2</mn> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi (t)={1 \over {{\sqrt {2\pi }}\sigma ^{3}}}\left(1-{t^{2} \over \sigma ^{2}}\right)e^{-t^{2} \over 2\sigma ^{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/023d891dbc508b7ac0e0472ff4719c5b904d4f6a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:30.803ex; height:7.009ex;" alt="{\displaystyle \psi (t)={1 \over {{\sqrt {2\pi }}\sigma ^{3}}}\left(1-{t^{2} \over \sigma ^{2}}\right)e^{-t^{2} \over 2\sigma ^{2}}}" /></span></dd></dl> <p>Contoh lain adalah fungsi dasar <a href="/wiki/Morlet" class="mw-redirect" title="Morlet">Morlet</a>, yang merupakan fungsi <a href="/wiki/Bilangan_kompleks" title="Bilangan kompleks">bilangan kompleks</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi _{\sigma }(t)=c_{\sigma }\pi ^{-{\frac {1}{4}}}e^{-{\frac {1}{2}}t^{2}}(e^{i\sigma t}-\kappa _{\sigma })}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ψ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>σ</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>σ</mi> </mrow> </msub> <msup> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> </mrow> </msup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </msup> <mo stretchy="false">(</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>σ</mi> <mi>t</mi> </mrow> </msup> <mo>−</mo> <msub> <mi>κ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>σ</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi _{\sigma }(t)=c_{\sigma }\pi ^{-{\frac {1}{4}}}e^{-{\frac {1}{2}}t^{2}}(e^{i\sigma t}-\kappa _{\sigma })}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c6654c145a13a79b421cf0c00ab0f86df2fe1f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:31.062ex; height:4.009ex;" alt="{\displaystyle \psi _{\sigma }(t)=c_{\sigma }\pi ^{-{\frac {1}{4}}}e^{-{\frac {1}{2}}t^{2}}(e^{i\sigma t}-\kappa _{\sigma })}" /></span></dd></dl> <p>dengan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \kappa _{\sigma }=e^{-{\frac {1}{2}}\sigma ^{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>κ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>σ</mi> </mrow> </msub> <mo>=</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \kappa _{\sigma }=e^{-{\frac {1}{2}}\sigma ^{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b3ed4cd1c225c8786bbd3368ad5132b4d5f3787" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.48ex; height:3.843ex;" alt="{\displaystyle \kappa _{\sigma }=e^{-{\frac {1}{2}}\sigma ^{2}}}" /></span> dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c_{\sigma }=\left(1+e^{-\sigma ^{2}}-2e^{-{\frac {3}{4}}\sigma ^{2}}\right)^{-{\frac {1}{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>σ</mi> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </msup> <mo>−</mo> <mn>2</mn> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </mrow> <msup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c_{\sigma }=\left(1+e^{-\sigma ^{2}}-2e^{-{\frac {3}{4}}\sigma ^{2}}\right)^{-{\frac {1}{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/518416757aafc5bdfd52ff16769d2e60d4a42982" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:29.956ex; height:7.176ex;" alt="{\displaystyle c_{\sigma }=\left(1+e^{-\sigma ^{2}}-2e^{-{\frac {3}{4}}\sigma ^{2}}\right)^{-{\frac {1}{2}}}}" /></span> </p> <div class="mw-heading mw-heading3"><h3 id="Transformasi_Wavelet_Diskrit">Transformasi Wavelet Diskrit</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wavelet&veaction=edit&section=4" title="Sunting bagian: Transformasi Wavelet Diskrit" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Wavelet&action=edit&section=4" title="Sunting kode sumber bagian: Transformasi Wavelet Diskrit"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dibandingkan dengan TWK, transformasi wavelet diskrit (TWD) dianggap relatif lebih mudah pengimplementasiannya. Prinsip dasar dari TWD adalah bagaimana cara mendapatkan representasi waktu dan skala dari sebuah sinyal menggunakan teknik pemfilteran digital dan operasi <a href="/w/index.php?title=Sub-sampling&action=edit&redlink=1" class="new" title="Sub-sampling (halaman belum tersedia)">sub-sampling</a>. </p><p>Sinyal pertama-tama dilewatkan pada rangkaian <a href="/w/index.php?title=Filter_high-pass&action=edit&redlink=1" class="new" title="Filter high-pass (halaman belum tersedia)">filter high-pass</a> dan low-pass, kemudian setengah dari masing-masing keluaran diambil sebagai sampel melalui operasi sub-sampling. Proses ini disebut sebagai proses dekomposisi satu tingkat. Keluaran dari filter low-pass digunakan sebagai masukkan di proses dekomposisi tingkat berikutnya. Proses ini diulang sampai tingkat proses dekomposisi yang diinginkan. Gabungan dari keluaran-keluaran filter high-pass dan satu keluaran <a href="/w/index.php?title=Filter_low-pass&action=edit&redlink=1" class="new" title="Filter low-pass (halaman belum tersedia)">filter low-pass</a> yang terakhir, disebut sebagai koefisien wavelet, yang berisi informasi sinyal hasil transformasi yang telah terkompresi. </p><p>Berkat operasi sub-sampling yang menghilangkan informasi sinyal yang berlebihan, transformasi wavelet telah menjadi salah satu metode <a href="/wiki/Kompresi_data" title="Kompresi data">kompresi data</a> yang paling handal. Biro investigasi federal (<a href="/wiki/FBI" class="mw-redirect" title="FBI">FBI</a>) <a href="/wiki/Amerika_Serikat" title="Amerika Serikat">Amerika Serikat</a> menggunakan metode ini dalam proses kompresi data <a href="/wiki/Sidik_jari" title="Sidik jari">sidik jari</a> mereka. </p><p>Pasangan filter high-pass dan low-pass yang digunakan harus merupakan <a href="/w/index.php?title=Quadrature_mirror_filter&action=edit&redlink=1" class="new" title="Quadrature mirror filter (halaman belum tersedia)">quadrature mirror filter</a> (QMF), yaitu pasangan filter yang memenuhi persamaan berikut: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h[L-1-n]=(-1)^{n}\cdot g[n]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mo stretchy="false">[</mo> <mi>L</mi> <mo>−</mo> <mn>1</mn> <mo>−</mo> <mi>n</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>⋅</mo> <mi>g</mi> <mo stretchy="false">[</mo> <mi>n</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h[L-1-n]=(-1)^{n}\cdot g[n]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b14a23ebbad72dbe36f85f79465e24c932463f23" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.034ex; height:2.843ex;" alt="{\displaystyle h[L-1-n]=(-1)^{n}\cdot g[n]}" /></span></dd></dl> <p>dengan h[n] adalah filtar high-pass, g[n] adalah filter low-pass dan L adalah panjang masing-masing filter. </p> <div class="mw-heading mw-heading2"><h2 id="Aplikasi">Aplikasi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wavelet&veaction=edit&section=5" title="Sunting bagian: Aplikasi" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Wavelet&action=edit&section=5" title="Sunting kode sumber bagian: Aplikasi"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r26333525" /><table class="box-Cleanup plainlinks metadata ambox ambox-style ambox-Cleanup" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Edit-clear.svg/40px-Edit-clear.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Edit-clear.svg/60px-Edit-clear.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Edit-clear.svg/80px-Edit-clear.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">artikel ini <b>perlu <a href="/wiki/Wikipedia:Merapikan_artikel" title="Wikipedia:Merapikan artikel">dirapikan</a></b> agar memenuhi <a href="/wiki/Wikipedia:Pedoman_gaya" title="Wikipedia:Pedoman gaya">standar Wikipedia</a>.<span class="hide-when-compact"> Tidak ada alasan yang diberikan. Silakan <a class="external text" href="https://id.wikipedia.org/w/index.php?title=Wavelet&action=edit">kembangkan artikel</a> ini semampu Anda. Merapikan artikel dapat dilakukan dengan <a href="/wiki/Bantuan:Wikifikasi" title="Bantuan:Wikifikasi">wikifikasi</a> atau membagi artikel ke paragraf-paragraf. Jika sudah dirapikan, silakan hapus templat ini.</span><span class="hide-when-compact"><i> (<small><a href="/wiki/Bantuan:Penghapusan_templat_pemeliharaan" class="mw-redirect" title="Bantuan:Penghapusan templat pemeliharaan">Pelajari cara dan kapan saatnya untuk menghapus pesan templat ini</a></small>)</i></span></div></td></tr></tbody></table> <p>TWK umumnya digunakan di dalam <a href="/wiki/Penelitian_ilmiah" title="Penelitian ilmiah">penelitian ilmiah</a> sedangkan TWD lebih banyak dipakai dalam aplikasi <a href="/wiki/Teknik" class="mw-redirect" title="Teknik">teknik</a> dan <a href="/wiki/Komputer" title="Komputer">komputer</a>. </p><p>Beberapa contoh aplikasi: </p> <div class="mw-heading mw-heading3"><h3 id="TWK">TWK</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wavelet&veaction=edit&section=6" title="Sunting bagian: TWK" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Wavelet&action=edit&section=6" title="Sunting kode sumber bagian: TWK"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Fisika" title="Fisika">Fisika</a> <ul><li><a href="/wiki/Mekanika_kuantum" title="Mekanika kuantum">Mekanika kuantum</a></li> <li><a href="/wiki/Geofisika" title="Geofisika">Geofisika</a></li> <li><a href="/wiki/Turbulensi" title="Turbulensi">Turbulensi</a></li></ul></li> <li><a href="/wiki/Kimia" title="Kimia">Kimia</a></li> <li><a href="/wiki/Biologi" title="Biologi">Biologi</a> <ul><li><a href="/wiki/EEG" class="mw-redirect" title="EEG">EEG</a></li> <li><a href="/w/index.php?title=ECG&action=edit&redlink=1" class="new" title="ECG (halaman belum tersedia)">ECG</a></li> <li>Analisis <a href="/wiki/Protein" title="Protein">protein</a> dan <a href="/wiki/DNA" class="mw-redirect" title="DNA">DNA</a></li></ul></li> <li>Teknik <ul><li><a href="/w/index.php?title=Respon_transien&action=edit&redlink=1" class="new" title="Respon transien (halaman belum tersedia)">Respon transien</a></li> <li><a href="/w/index.php?title=Respon_impuls&action=edit&redlink=1" class="new" title="Respon impuls (halaman belum tersedia)">Respon impuls</a></li> <li>Analisis <a href="/w/index.php?title=Nilai_jenuh&action=edit&redlink=1" class="new" title="Nilai jenuh (halaman belum tersedia)">nilai jenuh</a></li></ul></li> <li><a href="/wiki/Pengenalan_suara" class="mw-disambig" title="Pengenalan suara">Pengenalan suara</a></li></ul> <p><br /> </p> <div class="mw-heading mw-heading3"><h3 id="TWD">TWD</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wavelet&veaction=edit&section=7" title="Sunting bagian: TWD" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Wavelet&action=edit&section=7" title="Sunting kode sumber bagian: TWD"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Proses <a href="/w/index.php?title=De-noising&action=edit&redlink=1" class="new" title="De-noising (halaman belum tersedia)">de-noising</a> sinyal</li> <li><a href="/wiki/Kompresi_data" title="Kompresi data">Kompresi data</a></li> <li><a href="/w/index.php?title=Pengolahan_gambar&action=edit&redlink=1" class="new" title="Pengolahan gambar (halaman belum tersedia)">Pengolahan gambar</a></li> <li>Penghitungan <a href="/wiki/Matriks" class="mw-disambig" title="Matriks">matriks</a> <a href="/wiki/Nilai_eigen" class="mw-redirect" title="Nilai eigen">nilai eigen</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Lihat_pula">Lihat pula</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wavelet&veaction=edit&section=8" title="Sunting bagian: Lihat pula" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Wavelet&action=edit&section=8" title="Sunting kode sumber bagian: Lihat pula"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Transformasi_Fourier" title="Transformasi Fourier">Transformasi Fourier</a></li> <li><a href="/w/index.php?title=Transformasi_Fourier_waktu-singkat&action=edit&redlink=1" class="new" title="Transformasi Fourier waktu-singkat (halaman belum tersedia)">Transformasi Fourier waktu-singkat</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Referensi">Referensi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Wavelet&veaction=edit&section=9" title="Sunting bagian: Referensi" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Wavelet&action=edit&section=9" title="Sunting kode sumber bagian: Referensi"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://users.rowan.edu/~polikar/WAVELETS/WTtutorial.html">Wavelet Tutorial</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20180430090402/http://users.rowan.edu/~polikar/WAVELETS/WTtutorial.html">Diarsipkan</a> 2018-04-30 di <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.</li> <li><a rel="nofollow" class="external text" href="http://perso.orange.fr/polyvalens/clemens/wavelets/wavelets.html">A Very Friendly Guide to Wavelet</a></li> <li><a rel="nofollow" class="external text" href="http://www.bearcave.com/misl/misl_tech/wavelets/index.html">Wavelet and Signal Processing</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Pranala_luar">Pranala luar</h2><span 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