{"id":13562,"date":"2025-02-24T11:19:33","date_gmt":"2025-02-24T08:19:33","guid":{"rendered":"https:\/\/umram.bilkent.edu.tr\/index.php\/2025\/02\/24\/ortak-zaman-dugum-kesirli-fourier-donusumu\/"},"modified":"2026-11-04T10:57:24","modified_gmt":"2026-11-04T07:57:24","slug":"ortak-zaman-dugum-kesirli-fourier-donusumu","status":"publish","type":"post","link":"https:\/\/umram.bilkent.edu.tr\/index.php\/tr\/2025\/02\/24\/ortak-zaman-dugum-kesirli-fourier-donusumu\/","title":{"rendered":"Ortak zaman-d\u00fc\u011f\u00fcm kesirli Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc"},"content":{"rendered":"<p>Signal Processing dergisinde yay\u0131mlanan \u00e7al\u0131\u015fmam\u0131zda, geleneksel ortak zaman-d\u00fc\u011f\u00fcm analizini kesirli alana geni\u015fleten yeni bir \u00e7er\u00e7eve olan ortak zaman-d\u00fc\u011f\u00fcm kesirli Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc (JFRT) sunulmaktad\u0131r. Hem zaman hem de \u00e7izge alan\u0131nda kesirli dereceler kullanan JFRT, mevcut Fourier tabanl\u0131 y\u00f6ntemleri genellemekte ve g\u00fcr\u00fclt\u00fc giderme, s\u00fczge\u00e7leme ve k\u00fcmeleme gibi g\u00f6revlerde daha iyi ba\u015far\u0131m sa\u011flamaktad\u0131r.<\/p>\n<p>\u00d6ne \u00e7\u0131kan noktalar:<\/p><ul><li>Ortak zaman-d\u00fc\u011f\u00fcm sinyallerinin kesirli analizi i\u00e7in birle\u015fik bir yakla\u015f\u0131m.<\/li><li>\u0130ndis toplanabilirli\u011fi, tersinirlik ve birim d\u00f6n\u00fc\u015f\u00fcme indirgenme gibi kuramsal g\u00fcvenceler.<\/li><li>G\u00fcr\u00fclt\u00fcl\u00fc veriyi g\u00fcvenilir bi\u00e7imde i\u015fleyen, Tikhonov d\u00fczenlile\u015ftirmesine dayal\u0131 bir g\u00fcr\u00fclt\u00fc giderme y\u00f6ntemi.<\/li><li>En g\u00fcncel tekniklere g\u00f6re daha iyi sonu\u00e7lar g\u00f6steren kapsaml\u0131 say\u0131sal deneyler.<\/li><\/ul>\n\n<p>Makale: <a href=\"https:\/\/doi.org\/10.1016\/j.sigpro.2025.109944\" target=\"_blank\" rel=\"noopener\">https:\/\/doi.org\/10.1016\/j.sigpro.2025.109944<\/a><\/p>\n\n<p><strong>\u00d6zet:<\/strong><\/p>\n<p>\u00c7izge sinyal i\u015fleme (GSP), \u00e7izge d\u00fc\u011f\u00fcmleri \u00fczerinde tan\u0131ml\u0131 sinyalleri kullanarak \u00d6klid d\u0131\u015f\u0131 alanlardaki y\u00fcksek boyutlu verilerin analizini kolayla\u015ft\u0131r\u0131r. Dura\u011fan verinin yan\u0131 s\u0131ra her d\u00fc\u011f\u00fcm s\u00fcrekli zaman serisi sinyalleri de sa\u011flayabilir ve b\u00f6ylece \u00e7izge sinyalleri her d\u00fc\u011f\u00fcmde zaman serisine d\u00f6n\u00fc\u015f\u00fcr. Ortak zaman-d\u00fc\u011f\u00fcm Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc (JFT) \u00e7er\u00e7evesi bu sinyallerin spektral analizine olanak tan\u0131r. Kesirli Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fcn (FRT) s\u0131radan Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fc geni\u015fletmesine benzer bi\u00e7imde, bu \u00e7al\u0131\u015fmada JFT&#8217;nin bir genellemesi olarak ortak zaman-d\u00fc\u011f\u00fcm kesirli Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc (JFRT) tan\u0131t\u0131lmaktad\u0131r. JFRT, Fourier analizini hem zaman hem de d\u00fc\u011f\u00fcm alan\u0131nda kesirli derecelere geni\u015fleterek ortak zaman-d\u00fc\u011f\u00fcm i\u015flemede kesirli analizi m\u00fcmk\u00fcn k\u0131lar. JFRT&#8217;nin JFT&#8217;yi genelledi\u011fi ve belirli \u00e7izge topolojileri i\u00e7in indis toplanabilirli\u011fi, tersinirlik, birim d\u00f6n\u00fc\u015f\u00fcme indirgenme ve \u00fcniterlik \u00f6zelliklerini korudu\u011fu kuramsal olarak g\u00f6sterilmektedir. Ayr\u0131ca JFRT alan\u0131nda Tikhonov d\u00fczenlile\u015ftirmesine dayal\u0131, g\u00fcvenilir ve iyi davran\u0131\u015fl\u0131 \u00e7\u00f6z\u00fcmler veren bir g\u00fcr\u00fclt\u00fc giderme y\u00f6ntemi t\u00fcretilmektedir. Sentetik ve ger\u00e7ek veri setleri \u00fczerindeki kapsaml\u0131 say\u0131sal deneyler, JFRT&#8217;nin g\u00fcr\u00fclt\u00fc giderme ve k\u00fcmeleme g\u00f6revlerinde en g\u00fcncel yakla\u015f\u0131mlardan daha ba\u015far\u0131l\u0131 oldu\u011funu g\u00f6stermektedir.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Signal Processing dergisinde yay\u0131mlanan \u00e7al\u0131\u015fmam\u0131zda, geleneksel ortak zaman-d\u00fc\u011f\u00fcm analizini kesirli alana geni\u015fleten yeni bir \u00e7er\u00e7eve olan ortak zaman-d\u00fc\u011f\u00fcm kesirli Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc (JFRT) sunulmaktad\u0131r. Hem zaman hem de \u00e7izge alan\u0131nda kesirli dereceler kullanan JFRT, mevcut Fourier tabanl\u0131 y\u00f6ntemleri genellemekte ve g\u00fcr\u00fclt\u00fc giderme, s\u00fczge\u00e7leme ve k\u00fcmeleme gibi g\u00f6revlerde daha iyi ba\u015far\u0131m sa\u011flamaktad\u0131r. \u00d6ne \u00e7\u0131kan noktalar:Ortak zaman-d\u00fc\u011f\u00fcm sinyallerinin\u2026<\/p>\n","protected":false},"author":9,"featured_media":12650,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[445],"tags":[],"class_list":["post-13562","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\/13562","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=13562"}],"version-history":[{"count":1,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts\/13562\/revisions"}],"predecessor-version":[{"id":13563,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts\/13562\/revisions\/13563"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/media\/12650"}],"wp:attachment":[{"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/media?parent=13562"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/categories?post=13562"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/tags?post=13562"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}