{"id":13593,"date":"2021-02-01T09:16:11","date_gmt":"2021-02-01T06:16:11","guid":{"rendered":"https:\/\/umram.bilkent.edu.tr\/index.php\/2021\/02\/01\/operator-kuramina-dayali-ayrik-olcekleme\/"},"modified":"2026-11-04T11:00:05","modified_gmt":"2026-11-04T08:00:05","slug":"operator-kuramina-dayali-ayrik-olcekleme","status":"publish","type":"post","link":"https:\/\/umram.bilkent.edu.tr\/index.php\/tr\/2021\/02\/01\/operator-kuramina-dayali-ayrik-olcekleme\/","title":{"rendered":"Operat\u00f6r kuram\u0131na dayal\u0131 ayr\u0131k \u00f6l\u00e7ekleme"},"content":{"rendered":"<p>Ayr\u0131k sinyal \u00f6l\u00e7ekleme, merkezi \u00f6neme sahip temel bir i\u015flemdir ve genellikle bir arade\u011ferleme problemi olarak ele al\u0131nan \u00e7e\u015fitli g\u00fc\u00e7l\u00fckler i\u00e7erir. Geleneksel anlamda arade\u011ferleme i\u00e7ermeyen yakla\u015f\u0131m\u0131m\u0131z bu probleme yeni ve \u00f6zg\u00fcn bir bak\u0131\u015f a\u00e7\u0131s\u0131 getirmekte ve pek \u00e7ok kuramsal ve uygulamal\u0131 ba\u011flamda yararl\u0131 olabilmektedir. Hiperdiferansiyel operat\u00f6r kuram\u0131n\u0131n bir ayr\u0131k i\u015flemi tan\u0131mlama problemine uygulanmas\u0131n\u0131n, sinyal analizi ve i\u015fleme i\u00e7in \u00f6nemli olan ba\u015fka i\u015flemlerde de yeni ara\u015ft\u0131rma y\u00f6nleri a\u00e7abilece\u011fi d\u00fc\u015f\u00fcn\u00fclmektedir.<\/p>\n\n<p>Makale: <a href=\"https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S1051200420302499\" target=\"_blank\" rel=\"noopener\">https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S1051200420302499<\/a><\/p>\n\n<p><strong>\u00d6zet: <\/strong><\/p>\n<p>Sinyal \u00f6l\u00e7ekleme, bir sinyalin koordinat y\u00f6nleri boyunca geni\u015fletildi\u011fi ya da daralt\u0131ld\u0131\u011f\u0131, uygulamada \u00f6nemli temel bir i\u015flemdir. B\u00fcy\u00fctme ya da yak\u0131nla\u015ft\u0131rma olarak da adland\u0131r\u0131lan \u00f6l\u00e7ekleme, sinyal de\u011ferlerini yeni koordinat noktalar\u0131na ta\u015f\u0131makla yap\u0131lamad\u0131\u011f\u0131 i\u00e7in ayr\u0131k de\u011fi\u015fkenli sinyallerde karma\u015f\u0131kt\u0131r. Ayr\u0131k \u00f6l\u00e7eklemeye y\u00f6nelik uygulamadaki yakla\u015f\u0131mlar\u0131n \u00e7o\u011fu arade\u011ferleme i\u00e7erir. Bu \u00e7al\u0131\u015fmada geleneksel arade\u011ferleme i\u00e7ermeyen, hiperdiferansiyel operat\u00f6r kuram\u0131na dayal\u0131 yeni bir yakla\u015f\u0131m \u00f6nerilmektedir. Bu yakla\u015f\u0131m, ayr\u0131k Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc kuram\u0131yla tam tutarl\u0131, kendi i\u00e7inde tutarl\u0131 ve yal\u0131n bir ayr\u0131k \u00f6l\u00e7ekleme tan\u0131m\u0131 sa\u011flamaktad\u0131r. D\u00f6n\u00fc\u015f\u00fcm tasar\u0131m\u0131 gibi sinyal kuram\u0131 ve analizindeki ba\u015fka problemlere de uygulanabilir. Kuramsal zarafetinin yan\u0131 s\u0131ra say\u0131sal ger\u00e7ekle\u015ftirme i\u00e7in de bir temel sunmaktad\u0131r.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ayr\u0131k sinyal \u00f6l\u00e7ekleme, merkezi \u00f6neme sahip temel bir i\u015flemdir ve genellikle bir arade\u011ferleme problemi olarak ele al\u0131nan \u00e7e\u015fitli g\u00fc\u00e7l\u00fckler i\u00e7erir. Geleneksel anlamda arade\u011ferleme i\u00e7ermeyen yakla\u015f\u0131m\u0131m\u0131z bu probleme yeni ve \u00f6zg\u00fcn bir bak\u0131\u015f a\u00e7\u0131s\u0131 getirmekte ve pek \u00e7ok kuramsal ve uygulamal\u0131 ba\u011flamda yararl\u0131 olabilmektedir. Hiperdiferansiyel operat\u00f6r kuram\u0131n\u0131n bir ayr\u0131k i\u015flemi tan\u0131mlama problemine uygulanmas\u0131n\u0131n, sinyal analizi ve\u2026<\/p>\n","protected":false},"author":9,"featured_media":11278,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[445],"tags":[],"class_list":["post-13593","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\/13593","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=13593"}],"version-history":[{"count":1,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts\/13593\/revisions"}],"predecessor-version":[{"id":13594,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/posts\/13593\/revisions\/13594"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/media\/11278"}],"wp:attachment":[{"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/media?parent=13593"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/categories?post=13593"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/umram.bilkent.edu.tr\/index.php\/wp-json\/wp\/v2\/tags?post=13593"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}