{"id":13574,"date":"2024-08-09T09:44:46","date_gmt":"2024-08-09T06:44:46","guid":{"rendered":"https:\/\/umram.bilkent.edu.tr\/index.php\/2024\/08\/09\/cizge-kesirli-fourier-donusumu-birlesik-bir-kuram\/"},"modified":"2026-11-04T10:58:19","modified_gmt":"2026-11-04T07:58:19","slug":"cizge-kesirli-fourier-donusumu-birlesik-bir-kuram","status":"publish","type":"post","link":"https:\/\/umram.bilkent.edu.tr\/index.php\/tr\/2024\/08\/09\/cizge-kesirli-fourier-donusumu-birlesik-bir-kuram\/","title":{"rendered":"\u00c7izge kesirli Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc: Birle\u015fik bir kuram"},"content":{"rendered":"<p>Kesirli Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fc \u00e7izge alan\u0131na genelleyen \u201cGraph Fractional Fourier Transform: A Unified Theory\u201d ba\u015fl\u0131kl\u0131 \u00e7al\u0131\u015fmam\u0131z IEEE Transactions on Signal Processing dergisinde yay\u0131mlanm\u0131\u015ft\u0131r.<\/p>\n<p>\u00c7al\u0131\u015fman\u0131n ba\u015fl\u0131ca katk\u0131lar\u0131:<\/p>\n<ul>\n<li>\u00c7izge kesirli Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fcn (GFRFT) kesirli kuvvete dayal\u0131 tan\u0131m\u0131n\u0131n her \u00e7izge yap\u0131s\u0131n\u0131 ve d\u00f6n\u00fc\u015f\u00fcm derecesini kapsayacak bi\u00e7imde titizlikle geni\u015fletilmesi.<\/li>\n<li>Klasik FRFT kuram\u0131yla tutarl\u0131 olan ve b\u00fcy\u00fck \u00e7izgelerde daha h\u0131zl\u0131 hesaplama sa\u011flayan, hiperdiferansiyel operat\u00f6re dayal\u0131 yeni bir GFRFT tan\u0131m\u0131.<\/li>\n<li>D\u00f6n\u00fc\u015f\u00fcm derecesinin \u00f6\u011frenme yoluyla en uygun bi\u00e7imde se\u00e7ilmesini sa\u011flayan ve GFRFT&#8217;nin sinir a\u011flar\u0131 ile makine \u00f6\u011frenmesi uygulamalar\u0131nda kullan\u0131lmas\u0131n\u0131 m\u00fcmk\u00fcn k\u0131lan bir y\u00f6ntem.<\/li>\n<li>GFRFT tan\u0131mlar\u0131n\u0131n e\u015fde\u011ferli\u011fini ve g\u00fcr\u00fclt\u00fc giderme, s\u0131n\u0131fland\u0131rma ve \u00f6rnekleme g\u00f6revlerinde GFT ile di\u011fer \u00e7izge sinyal i\u015fleme y\u00f6ntemlerine g\u00f6re \u00fcst\u00fcnl\u00fc\u011f\u00fcn\u00fc g\u00f6steren kapsaml\u0131 deneyler.<\/li>\n<\/ul>\n\n<p>Makale: <a href=\"https:\/\/doi.org\/10.1109\/TSP.2024.3439211\" target=\"_blank\" rel=\"noopener\">https:\/\/doi.org\/10.1109\/TSP.2024.3439211<\/a><\/p>\n<p>Kod: <a href=\"https:\/\/github.com\/koc-lab\/gfrft-unified\" target=\"_blank\" rel=\"noopener\">https:\/\/github.com\/koc-lab\/gfrft-unified<\/a><\/p>\n\n<p><strong>\u00d6zet:<\/strong><\/p>\n<p>Kesirli Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc (FRFT), Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fc bir d\u00f6n\u00fc\u015f\u00fcm derecesiyle parametrik olarak genelleyerek sinyalleri ara zaman-frekans alanlar\u0131nda temsil eder. FRFT&#8217;nin Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fcn kesirli kuvveti, zaman-frekans d\u00fczleminde d\u00f6nd\u00fcrme ve hiperdiferansiyel operat\u00f6r gibi birbirine e\u015fde\u011fer bir\u00e7ok tan\u0131m\u0131 vard\u0131r ve her biri t\u00fcretme kolayl\u0131\u011f\u0131 ya da hesaplama verimlili\u011fi gibi \u00fcst\u00fcnl\u00fckler sunar. \u00c7izge sinyal i\u015fleme (GSP) ise geleneksel sinyal i\u015flemeyi d\u00fczensiz \u00e7izge yap\u0131lar\u0131 \u00fczerindeki verilere geni\u015fleterek \u00e7izge sinyalleri i\u00e7in \u00f6rnekleme, s\u00fczge\u00e7leme ve Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc gibi kavramlar\u0131 m\u00fcmk\u00fcn k\u0131lar. \u00c7izge kesirli Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc (GFRFT) k\u0131sa s\u00fcre \u00f6nce GSP alan\u0131na ta\u015f\u0131nm\u0131\u015ft\u0131r. Ancak bu geni\u015fletme yaln\u0131zca belirli \u00e7izge yap\u0131lar\u0131na ve s\u0131n\u0131rl\u0131 bir d\u00f6n\u00fc\u015f\u00fcm derecesi aral\u0131\u011f\u0131na dayanan kesirli kuvvet tan\u0131m\u0131n\u0131 genellemektedir. \u0130deal olarak GFRFT, olabildi\u011fince \u00e7ok say\u0131da alternatif tan\u0131mla tutarl\u0131 olmal\u0131d\u0131r. Bu \u00e7al\u0131\u015fmada \u00f6nce her \u00e7izge yap\u0131s\u0131n\u0131 ve d\u00f6n\u00fc\u015f\u00fcm derecesini destekleyen titiz bir kesirli kuvvet tabanl\u0131 GFRFT tan\u0131m\u0131 verilmektedir. Ard\u0131ndan b\u00fcy\u00fck \u00e7izgelerde ileri ve ters d\u00f6n\u00fc\u015f\u00fcm matrislerinin daha h\u0131zl\u0131 hesaplanmas\u0131n\u0131 sa\u011flayan, hiperdiferansiyel operat\u00f6re dayal\u0131 yeni GFRFT tan\u0131m\u0131 tan\u0131t\u0131lmaktad\u0131r. Bu tan\u0131m yoluyla d\u00f6n\u00fc\u015f\u00fcm derecesinin veriden \u00f6\u011frenilerek se\u00e7ilmesine dayanan yeni bir yakla\u015f\u0131m t\u00fcretilmektedir. Bant s\u0131n\u0131rl\u0131l\u0131k, s\u00fczge\u00e7ler ve di\u011fer d\u00f6n\u00fc\u015f\u00fcmlerle ili\u015fki gibi temel GSP kavramlar\u0131 da GFRFT ba\u011flam\u0131nda ele al\u0131nmaktad\u0131r. Son olarak g\u00fcr\u00fclt\u00fc giderme, s\u0131n\u0131fland\u0131rma ve \u00f6rnekleme g\u00f6revlerini i\u00e7eren kapsaml\u0131 deneylerle GFRFT&#8217;nin paralel tan\u0131mlar\u0131n\u0131n e\u015fde\u011ferli\u011fi, d\u00f6n\u00fc\u015f\u00fcm derecesinin \u00f6\u011frenilebilirli\u011fi ve GFRFT&#8217;nin GFT ile di\u011fer GSP y\u00f6ntemlerine g\u00f6re \u00fcst\u00fcnl\u00fc\u011f\u00fc g\u00f6sterilmektedir.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Kesirli Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fc \u00e7izge alan\u0131na genelleyen \u201cGraph Fractional Fourier Transform: A Unified Theory\u201d ba\u015fl\u0131kl\u0131 \u00e7al\u0131\u015fmam\u0131z IEEE Transactions on Signal Processing dergisinde yay\u0131mlanm\u0131\u015ft\u0131r. \u00c7al\u0131\u015fman\u0131n ba\u015fl\u0131ca katk\u0131lar\u0131: \u00c7izge kesirli Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fcn (GFRFT) kesirli kuvvete dayal\u0131 tan\u0131m\u0131n\u0131n her \u00e7izge yap\u0131s\u0131n\u0131 ve d\u00f6n\u00fc\u015f\u00fcm derecesini kapsayacak bi\u00e7imde titizlikle geni\u015fletilmesi. Klasik FRFT kuram\u0131yla tutarl\u0131 olan ve b\u00fcy\u00fck \u00e7izgelerde daha h\u0131zl\u0131 hesaplama\u2026<\/p>\n","protected":false},"author":9,"featured_media":12398,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[445],"tags":[],"class_list":["post-13574","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-duyurular"],"_links":{"self":[{"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts\/13574","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/comments?post=13574"}],"version-history":[{"count":1,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts\/13574\/revisions"}],"predecessor-version":[{"id":13575,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts\/13574\/revisions\/13575"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/media\/12398"}],"wp:attachment":[{"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/media?parent=13574"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/categories?post=13574"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/tags?post=13574"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}