{"id":1168,"date":"2023-04-16T12:58:54","date_gmt":"2023-04-16T09:58:54","guid":{"rendered":"https:\/\/legendhomework.com\/tr\/?p=1168"},"modified":"2023-04-16T12:58:54","modified_gmt":"2023-04-16T09:58:54","slug":"haar-dalgaciklari-multimedya-bolumu-multimedya-bolumu-odevleri-multimedya-bolumu-tez-yaptirma-multimedya-bolumu-odev-ucretleri","status":"publish","type":"post","link":"https:\/\/legendhomework.com\/tr\/haar-dalgaciklari-multimedya-bolumu-multimedya-bolumu-odevleri-multimedya-bolumu-tez-yaptirma-multimedya-bolumu-odev-ucretleri\/","title":{"rendered":"Haar Dalgac\u0131klar\u0131 \u2013 Multimedya B\u00f6l\u00fcm\u00fc \u2013 Multimedya B\u00f6l\u00fcm\u00fc \u00d6devleri \u2013 Multimedya B\u00f6l\u00fcm\u00fc Tez Yapt\u0131rma \u2013Multimedya B\u00f6l\u00fcm\u00fc \u00d6dev \u00dccretleri\u00a0"},"content":{"rendered":"

Haar Dalgac\u0131klar\u0131na Dayal\u0131 D\u00f6n\u00fc\u015f\u00fcm<\/span><\/strong><\/h3>\n

\u00d6nceki b\u00f6l\u00fcmlerde dalgac\u0131k teorisinin tart\u0131\u015f\u0131lmas\u0131ndan sonra, bu b\u00f6l\u00fcm Haar dalgac\u0131\u011f\u0131 ile h\u0131zl\u0131 dalgac\u0131k d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fc \u00f6rneklemektedir. Haar d\u00f6n\u00fc\u015f\u00fcm\u00fc, do\u011fas\u0131 gere\u011fi sezgisel bir yorum i\u00e7erdi\u011finden, bir dalgac\u0131k d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fcn felsefesini ve do\u011fas\u0131n\u0131 tan\u0131tmak i\u00e7in uygundur.<\/span><\/p>\n

Bu b\u00f6l\u00fcm\u00fc anlamak i\u00e7in \u00f6nceden dalgac\u0131k teorisi bilgisi gerekli de\u011fildir. Ancak bu b\u00f6l\u00fcm\u00fcn sonunda bu \u00f6rnek ile genel teori aras\u0131ndaki bo\u015flu\u011fu dolduraca\u011f\u0131z. K\u0131sa bir bak\u0131\u015f olarak, bu b\u00f6l\u00fcmde kar\u015f\u0131la\u015f\u0131lan s\u00fczge\u00e7ler, tart\u0131\u015f\u0131lan ortogonal dalgac\u0131k s\u00fczge\u00e7lerinin genel ba\u011flam\u0131na yerle\u015ftirilecektir.<\/span><\/p>\n

\u00d6rnekleme mesafesi olan tek boyutlu ayr\u0131 bir sinyale (\u00f6rne\u011fin bir ses sinyali) sahip oldu\u011fumuzu varsayal\u0131m. Ama\u00e7, dalgac\u0131k d\u00f6n\u00fc\u015f\u00fcm\u00fc arac\u0131l\u0131\u011f\u0131yla zaman \u00f6l\u00e7e\u011fi alan\u0131nda katsay\u0131lara ayr\u0131\u015ft\u0131rmakt\u0131r.<\/span><\/p>\n

Bu nedenle, sinyali ‘ili\u015fkisizle\u015ftirebilen’ bir algoritma ile ilgileniyoruz. Ba\u015fka bir deyi\u015fle, ayn\u0131 bilgiyi daha az katsay\u0131l\u0131 bir sinyalle, yani daha b\u00fcy\u00fck \u00f6rnekleme mesafesine sahip katsay\u0131larla ifade etmek isteriz.<\/span><\/p>\n

Daha kaba sinyalin sinyali tam olarak temsil etmeyece\u011fini kabul etsek de, en az\u0131ndan kabul edilebilir bir hata ile bir yakla\u015f\u0131m\u0131 temsil etmelidir, yani yakla\u015f\u0131k sinyal ile orijinal aras\u0131ndaki fark k\u00fc\u00e7\u00fck olmal\u0131d\u0131r. Son olarak, hatan\u0131n izini s\u00fcrebilece\u011fimizi talep ediyoruz. Bu nedenle, daha az katsay\u0131 kullanarak kaybolan bilgiler \u00fczerinde kesin kontrole sahip olmak istiyoruz.<\/span><\/p>\n

\u0130lk giri\u015fim ve en sezgisel olan\u0131 \u00f6rnek say\u0131s\u0131n\u0131 fakt\u00f6re g\u00f6re azaltmak ve her iki kom\u015fu \u00f6rne\u011fin yakla\u015f\u0131kl\u0131k olarak adland\u0131raca\u011f\u0131m\u0131z ortalama de\u011ferini hesaplamakt\u0131r.<\/span><\/p>\n

Filtreler cinsinden ifade edildi\u011finde, yakla\u015f\u0131kl\u0131k hesaplamas\u0131 ile ger\u00e7ekle\u015ftirilir. Kaybolan bilgi, orijinal sinyal de\u011feri ile bu ortalama aras\u0131ndaki farkt\u0131r.<\/span><\/p>\n

Her bir \u00e7iftin birinci de\u011feri ile yakla\u015f\u0131m aras\u0131ndaki fark\u0131n, kendisi ile her bir \u00e7iftin ikinci de\u011feri aras\u0131ndaki fark\u0131n negatifi oldu\u011funa dikkat edin. Bu nedenle detay olarak adland\u0131raca\u011f\u0131m\u0131z iki farktan birini saklamak yeterlidir. Bu detaylar verilmi\u015ftir. Detay hesaplamas\u0131 i\u00e7in filtre verilmi\u015ftir.<\/span><\/p>\n

Ayr\u0131ca, orijinal sinyali tan\u0131mlamak i\u00e7in gereken toplam katsay\u0131 say\u0131s\u0131n\u0131n de\u011fi\u015fmedi\u011fini de g\u00f6sterir. \u00d6rne\u011fimizdeki orijinal \u00f6rnekler, yakla\u015f\u0131k katsay\u0131lar ve detay katsay\u0131lar\u0131 ile de\u011fi\u015ftirilmi\u015ftir. Yaln\u0131zca “koordinat sistemi” de\u011fi\u015fti, yani incelenmekte olan temeli de\u011fi\u015ftirdik.<\/span><\/p>\n

Orijinal sinyale yakla\u015fma ve ayr\u0131nt\u0131lar\u0131 birbirinden ay\u0131rma i\u015flemi \u015fimdi yakla\u015f\u0131mlar \u00fczerinde tekrarlan\u0131r.\u00d6rnek sinyalimizde s\u0131ras\u0131yla ilk iki, \u00fc\u00e7 yineleme ad\u0131m\u0131n\u0131 g\u00f6sterin. B\u00f6l\u00fcm 1.6.3’te g\u00f6sterdi\u011fimiz gibi, d\u00f6n\u00fc\u015ft\u00fcr\u00fclm\u00fc\u015f uzay\u0131n tek bir katsay\u0131s\u0131n\u0131n orijinal sinyal \u00fczerindeki etkisi, iterasyon derinli\u011fi artt\u0131k\u00e7a geni\u015fler. Burada, \u00e7oklu \u00e7\u00f6z\u00fcn\u00fcrl\u00fck kavram\u0131n\u0131 kurtar\u0131yoruz.<\/span><\/p>\n

\u015eimdiye kadar ger\u00e7ekle\u015ftirilen ad\u0131mlar ayr\u0131\u015ft\u0131rma veya analizin bir par\u00e7as\u0131d\u0131r. Bununla birlikte, sentez, yani orijinal sinyalin d\u00f6n\u00fc\u015ft\u00fcr\u00fclm\u00fc\u015f uzaydaki katsay\u0131lar\u0131ndan yeniden olu\u015fturulmas\u0131 kolayd\u0131r. \u00d6rnek sinyalimizin ilk yinelemesinde hesaplamay\u0131 detayland\u0131r\u0131yoruz. Sinyalimizin ilk iki \u00f6rne\u011fini kurtarmak i\u00e7in, ilk yakla\u015f\u0131m ve detay de\u011ferlerini, yani yakla\u015f\u0131kl\u0131k ve detay olarak ele al\u0131yoruz.<\/span><\/p>\n

\n

Dalgac\u0131k<\/a> d\u00f6n\u00fc\u015f\u00fcm\u00fc Nedir<\/span>
\nHaar wavelet<\/span>
\nAyr\u0131k dalgac\u0131k d\u00f6n\u00fc\u015f\u00fcm\u00fc<\/span>
\n2d wavelet transform – matlab<\/span>
\nHaar wavelet filter coefficients<\/span>
\nGibbs phenomenon<\/span>
\nWalsh function<\/span>
\nOrthogonal basis functions<\/span><\/p>\n

\n

Benzer \u015fekilde, \u00fc\u00e7\u00fcnc\u00fc ve d\u00f6rd\u00fcnc\u00fc sinyal giri\u015flerinin sentezleri, ikinci yakla\u015f\u0131mdan (yani, ) ve ikinci detaydan (yani, ) elde edilir. Kar\u015f\u0131l\u0131k gelen filtreler, her \u00e7iftin birinci de\u011ferinin sentezi ve her \u00e7iftin ikinci de\u011ferinin sentezi i\u00e7indir.<\/span><\/p>\n

Toplamda, Haar d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fc tek boyutlu ayr\u0131k bir sinyal \u00fczerinde ger\u00e7ekle\u015ftirdik. Yakla\u015f\u0131m ve detay olarak yorumlama sezgiseldir. Katsay\u0131lar\u0131n toplam say\u0131s\u0131n\u0131n d\u00f6n\u00fc\u015f\u00fcm taraf\u0131ndan de\u011fi\u015fmeden kald\u0131\u011f\u0131n\u0131 g\u00f6rd\u00fck, bu da ona neden temel d\u00f6n\u00fc\u015f\u00fcm dedi\u011fimiz a\u00e7\u0131kl\u0131yor.<\/span><\/p>\n

Ayr\u0131ca, analizin iki filtre gerektirdi\u011fini g\u00f6rd\u00fck; bir yakla\u015f\u0131m (yani al\u00e7ak ge\u00e7iren) filtre ve bir detay (yani y\u00fcksek ge\u00e7iren) filtre. Sentez ayr\u0131ca, biri \u00e7ift \u00f6rneklerin sentezi (yani, ters d\u00fc\u015f\u00fck ge\u00e7i\u015f filtresi) ve biri tek \u00f6rneklerin sentezi (yani, ters y\u00fcksek ge\u00e7i\u015f filtresi) i\u00e7in olmak \u00fczere iki filtre gerektirir. Son olarak prosed\u00fcr\u00fcn kay\u0131ps\u0131z oldu\u011funu g\u00f6rd\u00fck.<\/span><\/p>\n

Haar d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fcn \u00e7ok \u00f6l\u00e7ekli analizle olu\u015fturulan ve Denklemler (1.10)\u2013(1.12) ve (1.17)\u2013(1.19) ile karakterize edilen filtre maskelerine ba\u011flanmas\u0131 h\u0131zl\u0131 bir \u015fekilde yap\u0131l\u0131r. Yukar\u0131daki Haar analiz ve sentez filtreleri, y\u00fcksek ge\u00e7i\u015f filtresinin katsay\u0131lar\u0131 i\u00e7in ko\u015fulu (1.17) zaten yerine getiriyor.<\/span><\/p>\n

Bu formda, filtre katsay\u0131lar\u0131n\u0131n do\u011frudan yorumu ortadan kalkm\u0131\u015ft\u0131r. Bununla birlikte, filtre katsay\u0131lar\u0131, bir sonraki b\u00f6l\u00fcmde sunulan genel teoriye m\u00fckemmel bir \u015fekilde uyar. Literat\u00fcrde, Haar dalgac\u0131k filtresi her iki yaz\u0131da da bulunabilir.<\/span><\/p>\n

Filtreleme<\/span><\/strong><\/h3>\n

Filtre k\u00fcmelerinin anla\u015f\u0131lmas\u0131, al\u00e7ak ge\u00e7iren ve y\u00fcksek ge\u00e7iren filtrelerin ve bunlar\u0131n tasar\u0131m\u0131n\u0131n derinlemesine anla\u015f\u0131lmas\u0131 i\u00e7in \u00e7ok \u00f6nemlidir. Bu b\u00f6l\u00fcmde, filtre maskelerinin ve \u00e7ok \u00f6l\u00e7ekli analizin kar\u015f\u0131lamas\u0131 gereken ko\u015fullar\u0131 ayr\u0131nt\u0131l\u0131 olarak ele al\u0131yoruz.<\/span><\/p>\n

Filtre bankalar\u0131 teorisi, filtre kavram\u0131n\u0131 gerektirir. Bir bant-s\u0131n\u0131rl\u0131 fonksiyonu ele alarak ba\u015fl\u0131yoruz, yani onun Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc kompakt deste\u011fe sahiptir.<\/span><\/p>\n

D\u00fc\u015f\u00fck ge\u00e7i\u015f filtresi, y\u00fcksek frekanslar\u0131 ‘keserken’ bir sinyalin t\u00fcm d\u00fc\u015f\u00fck frekanslar\u0131n\u0131 de\u011fi\u015ftirmeden b\u0131rak\u0131r. Bu nedenle, ideal bir d\u00fc\u015f\u00fck ge\u00e7i\u015f filtresinin Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc, kesme frekans\u0131 ile ge\u00e7i\u015f frekans\u0131 aras\u0131nda ge\u00e7i\u015fe sahip de\u011fildir.<\/span><\/p>\n

Bir fonksiyona ideal bir al\u00e7ak ge\u00e7iren filtrenin uygulanmas\u0131, zaman alan\u0131ndaki evri\u015fime ve ard\u0131ndan frekans alan\u0131na d\u00f6n\u00fc\u015f\u00fcme kar\u015f\u0131l\u0131k gelen frekans uzay\u0131nda ve frekans\u0131n \u00e7arp\u0131lmas\u0131 anlam\u0131na gelir.<\/span><\/p>\n

\u0130deal Y\u00fcksek Ge\u00e7i\u015fli Filtre<\/span><\/strong><\/h3>\n

Al\u00e7ak ge\u00e7iren filtrenin tersine, y\u00fcksek ge\u00e7iren filtre bir sinyalin t\u00fcm y\u00fcksek frekanslar\u0131n\u0131 de\u011fi\u015ftirmeden b\u0131rak\u0131rken d\u00fc\u015f\u00fck frekanslar\u0131 “keser”. \u0130deal bir d\u00fc\u015f\u00fck ge\u00e7i\u015fli filtreye benzer \u015fekilde, ideal bir y\u00fcksek ge\u00e7i\u015fli filtre, kesme frekans\u0131 ile ge\u00e7i\u015f frekans\u0131 aras\u0131nda hi\u00e7bir ge\u00e7i\u015fe sahip olmayan Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc olarak tan\u0131mlan\u0131r.<\/span><\/p>\n

Tam sinyal art\u0131k tamamen al\u00e7ak ge\u00e7iren ve y\u00fcksek ge\u00e7iren filtrelenmi\u015f b\u00f6l\u00fcmlerinin toplam\u0131 olarak tan\u0131mlanabilir. Denklemler ile ve filtre, baz\u0131 hesaplamalar tamamland\u0131ktan sonra bu b\u00f6l\u00fcm\u00fcn tart\u0131\u015fmas\u0131n\u0131 maskeler.<\/span><\/p>\n

Pratik ama\u00e7lar i\u00e7in, Denklemin sonsuz toplam\u0131 yerine, sinyalin al\u00e7ak ge\u00e7iren ve y\u00fcksek ge\u00e7iren filtrelenmi\u015f par\u00e7alar\u0131n\u0131n sonlu bir toplam\u0131 olarak temsil edilmesi arzu edilir. Bu talep, ge\u00e7i\u015f frekans\u0131 ile kesme frekans\u0131 aras\u0131ndaki ge\u00e7i\u015fi art\u0131k ideal olmayan iki kanall\u0131 filtre bankalar\u0131n\u0131n in\u015fas\u0131n\u0131n yolunu a\u00e7ar.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Haar Dalgac\u0131klar\u0131na Dayal\u0131 D\u00f6n\u00fc\u015f\u00fcm \u00d6nceki b\u00f6l\u00fcmlerde dalgac\u0131k teorisinin tart\u0131\u015f\u0131lmas\u0131ndan sonra, bu b\u00f6l\u00fcm Haar dalgac\u0131\u011f\u0131 ile h\u0131zl\u0131 dalgac\u0131k d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fc \u00f6rneklemektedir. Haar d\u00f6n\u00fc\u015f\u00fcm\u00fc, do\u011fas\u0131 gere\u011fi sezgisel bir yorum i\u00e7erdi\u011finden, bir dalgac\u0131k d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fcn felsefesini ve do\u011fas\u0131n\u0131 tan\u0131tmak i\u00e7in uygundur. Bu b\u00f6l\u00fcm\u00fc anlamak i\u00e7in \u00f6nceden dalgac\u0131k teorisi bilgisi gerekli de\u011fildir. Ancak bu b\u00f6l\u00fcm\u00fcn sonunda bu \u00f6rnek ile genel teori…
Devam\u0131<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[3451,3452,3453],"tags":[3457,3456,3454,3459,3455,3458,3461,3460],"class_list":["post-1168","post","type-post","status-publish","format-standard","hentry","category-dalgacik-donusumu-nedir","category-haar-wavelet","category-haar-wavelet-filter-coefficients","tag-2d-wavelet-transform-matlab","tag-ayrik-dalgacik-donusumu","tag-dalgacik-donusumu-nedir","tag-gibbs-phenomenon","tag-haar-wavelet","tag-haar-wavelet-filter-coefficients","tag-orthogonal-basis-functions","tag-walsh-function"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t