{"id":1164,"date":"2023-04-16T12:38:36","date_gmt":"2023-04-16T09:38:36","guid":{"rendered":"https:\/\/legendhomework.com\/tr\/?p=1164"},"modified":"2023-04-16T12:38:36","modified_gmt":"2023-04-16T09:38:36","slug":"zaman-frekans-cozunurlugu-multimedya-bolumu-multimedya-bolumu-odevleri-multimedya-bolumu-tez-yaptirma-multimedya-bolumu-odev-ucretleri","status":"publish","type":"post","link":"https:\/\/legendhomework.com\/tr\/zaman-frekans-cozunurlugu-multimedya-bolumu-multimedya-bolumu-odevleri-multimedya-bolumu-tez-yaptirma-multimedya-bolumu-odev-ucretleri\/","title":{"rendered":"Zaman\u2013Frekans \u00c7\u00f6z\u00fcn\u00fcrl\u00fc\u011f\u00fc \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":"

Dalgac\u0131k D\u00f6n\u00fc\u015f\u00fcm\u00fc<\/span><\/strong><\/h3>\n

Sinyal i\u015flemenin amac\u0131, sinyal dedi\u011fimiz belirli bir fonksiyondan belirli bilgileri \u00e7\u0131karmakt\u0131r. Bu ama\u00e7la, temel olarak bir fikir vard\u0131r: uygun bir d\u00f6n\u00fc\u015f\u00fcm\u00fcn okumay\u0131, yani ilgili bilginin analizini kolayla\u015ft\u0131raca\u011f\u0131 beklentisiyle sinyali d\u00f6n\u00fc\u015ft\u00fcrmek gerekir.<\/span><\/p>\n

Elbette d\u00f6n\u00fc\u015f\u00fcm\u00fcn se\u00e7imi, ki\u015finin ilgilendi\u011fi bilginin do\u011fas\u0131na ba\u011fl\u0131d\u0131r. D\u00f6n\u00fc\u015f\u00fcmle ilgili ikinci bir talep, orijinal fonksiyonun sentezlenebilmesi, yani d\u00f6n\u00fc\u015ft\u00fcr\u00fclm\u00fc\u015f durumundan yeniden olu\u015fturulabilmesidir. Bu tersinmezlik iddias\u0131d\u0131r.<\/span><\/p>\n

Bu, dalgac\u0131klar\u0131n tan\u0131m\u0131n\u0131 ve do\u011fas\u0131n\u0131 incelemektedir. S\u00fcrekli dalgac\u0131k d\u00f6n\u00fc\u015f\u00fcm\u00fc sunulmakta ve en \u00f6nemli \u00f6zellikleri tart\u0131\u015f\u0131lmaktad\u0131r.<\/span><\/p>\n

\u00d6rnek Dalgac\u0131klar<\/span><\/strong><\/p>\n

Bir dalgac\u0131\u011f\u0131n tan\u0131m\u0131 o kadar geneldir ki, bir “dalgac\u0131k” \u00e7ok farkl\u0131 \u00f6zelliklere ve \u015fekillere sahip olabilir. Bu b\u00f6l\u00fcmde daha sonra g\u00f6rece\u011fimiz gibi, \u00e7ok \u00f6l\u00e7ekli analiz, dalgac\u0131klar\u0131 s\u0131ras\u0131yla y\u00fcksek ge\u00e7iren filtrelere, bant ge\u00e7iren filtrelere ba\u011flar. Filtre bankalar\u0131n\u0131n teorisi ayr\u0131nt\u0131l\u0131d\u0131r. A\u015fa\u011f\u0131da, en yayg\u0131n dalgac\u0131klardan baz\u0131lar\u0131n\u0131 ve bunlar\u0131n Fourier d\u00f6n\u00fc\u015f\u00fcmlerini sunuyoruz.<\/span><\/p>\n

Nerede en y\u00fcksek ve ikinci en y\u00fcksek maksimumun oran\u0131 yeterince b\u00fcy\u00fck olacak \u015fekilde s\u0131kl\u0131kla se\u00e7ilen bir sabittir. Uygulamada, genellikle . Bu de\u011fer i\u00e7in Denk.(1.3)’deki ikinci terim pratikte ihmal edilebilecek kadar k\u00fc\u00e7\u00fckt\u00fcr. Dalgac\u0131\u011f\u0131n ger\u00e7ek k\u0131sm\u0131n\u0131n \u015fekli g\u00f6sterilmi\u015ftir.<\/span><\/p>\n

Daubechies Dalgac\u0131k<\/span><\/strong><\/p>\n

Daubechies dalgac\u0131k ailesi, \u00e7o\u011funlukla multimedya uygulamalar\u0131 i\u00e7in kullan\u0131l\u0131r. Genel teorisi \u00f6zetlenen e\u015flenik kareleme filtrelerinin belirli bir olu\u015fumudur.<\/span><\/p>\n

Daubechies dalgac\u0131klar\u0131 yineleme ile elde edilir; kapal\u0131 temsil yoktur. Daubechies dalgac\u0131klar\u0131, belirli bir say\u0131da kaybolma momenti2 i\u00e7in kompakt olarak desteklenen en k\u0131sa ortogonal dalgac\u0131klard\u0131r. Kaybolan momentlerin derecesi, filtre bankas\u0131 katsay\u0131lar\u0131n\u0131n miktar\u0131n\u0131 belirler.<\/span><\/p>\n

\u0130ntegral Dalgac\u0131k D\u00f6n\u00fc\u015f\u00fcm\u00fc<\/span><\/strong><\/p>\n

Denklem g\u00f6stermek i\u00e7in, kompakt olarak desteklenen bir dalgac\u0131\u011f\u0131n etkilerini detayland\u0131r\u0131yoruz. \u00c7eviri parametresi dalgac\u0131\u011f\u0131, zaman yerel bilgisini i\u00e7erecek \u015fekilde kayd\u0131r\u0131r. Parametre, etki alan\u0131n\u0131 y\u00f6netir: ile, dalgac\u0131k d\u00f6n\u00fc\u015f\u00fcm\u00fc, zaman-\u00e7\u00f6z\u00fcn\u00fcrl\u00fc\u011f\u00fc bulan\u0131kla\u015ft\u0131r\u0131rken konuma ‘yak\u0131nla\u015ft\u0131r\u0131r’. Geni\u015fletme ve \u00f6telemenin ard\u0131ndaki fikri g\u00f6sterir.<\/span><\/p>\n

Bir sinyalin dalgac\u0131k d\u00f6n\u00fc\u015f\u00fcm\u00fc, sinyali dalgac\u0131k yard\u0131m\u0131yla inceler. Ba\u015fka bir deyi\u015fle, ve ‘nin -\u00f6l\u00e7ekli \u00e7arp\u0131mlar\u0131 olu\u015fturulur, bu da ‘nin geni\u015fletilmi\u015f ve terc\u00fcme edilmi\u015f versiyonlar\u0131n\u0131 g\u00f6sterir. Hen\u00fcz bir dalgac\u0131k baz\u0131n\u0131n belirtilmedi\u011fini not etmek \u00f6nemlidir. Dalgac\u0131k d\u00f6n\u00fc\u015f\u00fcm teorisi, dalgac\u0131klar\u0131n genel \u00f6zelliklerine dayan\u0131r. \u0130htiya\u00e7lara g\u00f6re dalgac\u0131klar\u0131n tan\u0131mlanabilece\u011fi bir \u00e7er\u00e7evedir.<\/span><\/p>\n

Bir dalgac\u0131k d\u00f6n\u00fc\u015f\u00fcm\u00fc, bir sinyali kar\u015f\u0131l\u0131k gelen bir dalgac\u0131k i\u00e7in katsay\u0131lara ayr\u0131\u015ft\u0131r\u0131r. T\u00fcm dalgac\u0131klar ‘canl\u0131’ oldu\u011fundan, her fonksiyonun keyfi bir hassasiyetle tahmin edilip edilemeyece\u011fini bilmek isteriz.<\/span><\/p>\n

Ayr\u0131ca, dalgac\u0131k baz\u0131n\u0131n \u00f6zel bir g\u00f6r\u00fcn\u00fcme sahip olmas\u0131n\u0131 talep edebiliriz: K\u00fcme bir dalgac\u0131k baz\u0131ndad\u0131r; dalgac\u0131\u011f\u0131n geni\u015fletilmi\u015f ve \u00f6telenmi\u015f versiyonlar\u0131n\u0131 ifade eder. B\u00f6ylece, t\u00fcm fonksiyonlara bir dizi dalgac\u0131k katsay\u0131lar\u0131 ile yakla\u015fabiliriz.<\/span><\/p>\n

Denklem (1.5), her kare integrallenebilir fonksiyonun yaln\u0131zca bir dalgac\u0131\u011f\u0131n geni\u015fletilmi\u015f ve \u00f6telenmi\u015f versiyonlar\u0131 ile yakla\u015f\u0131k olarak tahmin edilebilece\u011fini s\u00f6yl\u00fcyor. D\u00fc\u015f\u00fcncelerimizin bu dalgac\u0131k s\u0131n\u0131f\u0131na odaklanmas\u0131n\u0131n nedeni budur. \u0130\u00e7inde ayr\u0131ca, hi\u00e7bir bilginin kaybolmamas\u0131 ve dalgac\u0131k d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fcn tersine \u00e7evrilebilir olmas\u0131 \u00f6zelli\u011fini korurken geni\u015fleme ve \u00f6teleme parametrelerinin g\u00fc\u00e7l\u00fc bir \u015fekilde k\u0131s\u0131tlanabilece\u011fini g\u00f6rece\u011fiz. Bu, h\u0131zl\u0131 dalgac\u0131k d\u00f6n\u00fc\u015f\u00fcm\u00fcne yol a\u00e7ar.<\/span><\/p>\n

\n

Nyquist \u00d6RNEKLEME frekans\u0131<\/span>
\nMinimum \u00f6rnekleme<\/a> frekans\u0131<\/span>
\nDijital \u00f6rnekleme nedir<\/span>
\nNyquist \u00f6rnekleme frekans\u0131 hesaplama<\/span>
\n\u00d6rnekleme frekans\u0131 form\u00fcl\u00fc<\/span>
\n\u00d6RNEKLEME teoremi<\/span>
\nNyquist Teoremi<\/span>
\n\u00d6rnekleme frekans\u0131 Nedir<\/span><\/p>\n

\n

Zaman\u2013Frekans \u00c7\u00f6z\u00fcn\u00fcrl\u00fc\u011f\u00fc<\/span><\/strong><\/h3>\n

\u00d6nceki b\u00f6l\u00fcmlerde, dalgac\u0131k d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fcn tek boyutlu bir sinyali zaman ve frekans olmak \u00fczere iki boyuta ayr\u0131\u015ft\u0131rd\u0131\u011f\u0131ndan bahsetmi\u015ftik. Ayr\u0131ca, bir dalgac\u0131\u011f\u0131n se\u00e7ilen bir frekansa ‘yak\u0131nla\u015ft\u0131\u011f\u0131n\u0131’ g\u00f6sterdik. Bu b\u00f6l\u00fcm, bu yak\u0131nla\u015ft\u0131rma \u00f6zelli\u011finin arka plan\u0131n\u0131 detayland\u0131rmaktad\u0131r. K\u0131sa s\u00fcreli Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc ile bir kar\u015f\u0131la\u015ft\u0131rma, iki yakla\u015f\u0131m aras\u0131ndaki ortak \u00f6zellikleri ve ayn\u0131 zamanda farkl\u0131l\u0131klar\u0131 da g\u00f6sterir.<\/span><\/p>\n

Heisenberg’in Belirsizlik \u0130lkesi<\/span><\/strong><\/p>\n

Enerjisi zamanda iyi bir \u015fekilde lokalize olan bir sinyalin, enerjisi iyi bir \u015fekilde k\u00fc\u00e7\u00fck bir frekansta yo\u011funla\u015fm\u0131\u015f bir Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fcne sahip olmas\u0131, bir sinyalin zaman-frekans analizinin g\u00fczel bir \u00f6zelli\u011fi olacakt\u0131r.<\/span><\/p>\n

Zaman yay\u0131l\u0131m\u0131n\u0131 azaltmak i\u00e7in bir \u00f6l\u00e7ekleme fakt\u00f6r\u00fc eklenir. ) ile i\u015faretlersek ve sinyalin toplam enerjisini toplam tutmay\u0131 ama\u00e7l\u0131yoruz.<\/span><\/p>\n

Bu, zaman an\u0131na b\u00f6l\u00fcnerek zaman i\u00e7inde kazan\u0131lan yerelle\u015ftirme miktar\u0131n\u0131n frekans \u00e7\u00f6z\u00fcn\u00fcrl\u00fc\u011f\u00fcnde kayboldu\u011fu anlam\u0131na gelir. Altta yatan ilke, zaman ve frekans lokalizasyonu aras\u0131ndaki de\u011fi\u015f toku\u015ftur. Bu ilke Heisenberg taraf\u0131ndan kuantum mekani\u011fi \u00fczerine yapt\u0131\u011f\u0131 \u00e7al\u0131\u015fmalar s\u0131ras\u0131nda ke\u015ffedilmi\u015f ve kan\u0131tlanm\u0131\u015ft\u0131r.<\/span><\/p>\n

Ayr\u0131ca, ula\u015f\u0131labilir kesinlik i\u00e7in bir alt s\u0131n\u0131r mevcuttur. Heisenberg Belirsizlik \u0130lkesi bunu belirtir.\u00a0<\/span>K\u0131sa s\u00fcreli Fourier analizi i\u00e7in, integral Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc sinyali frekanslar\u0131na ayr\u0131\u015ft\u0131rmadan \u00f6nce sinyal ger\u00e7ek ve simetrik bir pencere ile \u00e7arp\u0131l\u0131r. Pencere ” ile \u00e7evrilir ve mod\u00fcle edilir.<\/span><\/p>\n

Pencereli veya k\u0131sa s\u00fcreli Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc (STFT) kavram\u0131, “ile \u00e7arpman\u0131n Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fc kom\u015fulu\u011funda yerelle\u015ftirmesi” ger\u00e7e\u011finden kaynaklan\u0131r. B\u00f6ylece STFT, Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc i\u00e7in mevcut olmayan bir \u00f6zellik olan belirli bir zaman penceresi i\u00e7inde bir frekans fenomeninin lokalizasyonuna izin verir.<\/span><\/p>\n

Dalgac\u0131k d\u00f6n\u00fc\u015f\u00fcm\u00fc ile Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc aras\u0131ndaki kar\u015f\u0131la\u015ft\u0131rmalar\u0131n genellikle STFT’nin \u00f6zel durumuyla s\u0131n\u0131rl\u0131 olmas\u0131n\u0131n nedeni budur.<\/span><\/p>\n

STFT i\u00e7in zaman-frekans belirsizli\u011finin Heisenberg kutular\u0131n\u0131n hesaplanmas\u0131 a\u015fa\u011f\u0131dakileri ortaya \u00e7\u0131kar\u0131r: Pencere \u00e7ifttir, bu nedenle ” merkezlidir ve etraf\u0131ndaki zaman yay\u0131l\u0131m\u0131 ” ba\u011f\u0131ms\u0131zd\u0131r.<\/span><\/p>\n

Sonu\u00e7 olarak, \u00e7evrilmi\u015f ve mod\u00fcle edilmi\u015f pencerenin Heisenberg kutusu, “# .Bu kutunun boyutu ba\u011f\u0131ms\u0131zd\u0131r” ve# merkezli bir alana sahiptir. Bu, k\u0131sa s\u00fcreli bir Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fcn zaman-frekans d\u00fczleminde ayn\u0131 \u00e7\u00f6z\u00fcn\u00fcrl\u00fc\u011fe sahip oldu\u011fu anlam\u0131na gelir.<\/span><\/p>\n

Dalgac\u0131k D\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fcn \u00d6rnekleme Izgaras\u0131<\/span><\/strong><\/h3>\n

Bu b\u00f6l\u00fcmde, minimum art\u0131kl\u0131kla dalgac\u0131k d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fcn tersinirli\u011fi sorununu tart\u0131\u015faca\u011f\u0131z. Dalgac\u0131k d\u00f6n\u00fc\u015f\u00fcm\u00fcnden orijinal sinyali yeniden olu\u015fturabilmek i\u00e7in hangi ko\u015fullar\u0131n kar\u015f\u0131lanmas\u0131 gerekti\u011fi ve yeniden yap\u0131land\u0131rma i\u00e7in her bir dilatasyon ve \u00f6teleme parametresi \u00e7iftinin bilinmesinin gerekip gerekmedi\u011fi gibi sorular bu b\u00f6l\u00fcm\u00fc motive eder.<\/span><\/p>\n

Denklem’de, tek bir dalgac\u0131\u011f\u0131n geni\u015fletilmi\u015f ve \u00f6telenmi\u015f versiyonlar\u0131n\u0131n k\u00fcmesinin ‘de bir temel olu\u015fturdu\u011funu g\u00f6rd\u00fck. MalHas, dalgac\u0131\u011f\u0131n geni\u015flemesini y\u00f6nlendiren parametrenin daha da k\u0131s\u0131tlanabilece\u011fini g\u00f6stermi\u015ftir.<\/span><\/p>\n

Bir dalgac\u0131\u011f\u0131n Fourier d\u00f6n\u00fc\u015f\u00fcm\u00fc sonlu deste\u011fe sahipse, bu bant s\u0131n\u0131rl\u0131 fonksiyon bilgi kayb\u0131 olmadan \u00f6rneklenebilir. Shannon’\u0131n \u00f6rnekleme teoremi, m\u00fckemmel yeniden yap\u0131land\u0131rmaya izin vermek i\u00e7in gerekli olan kritik \u00f6rnekleme oran\u0131n\u0131 verir.<\/span><\/p>\n

Bant-s\u0131n\u0131rl\u0131 bir dalgac\u0131\u011f\u0131n her geni\u015fletilmi\u015f versiyonu yine bant-s\u0131n\u0131rl\u0131d\u0131r ve bu nedenle bir \u00f6rnekleme frekans\u0131 ile bilgi kayb\u0131 olmadan \u00f6rneklenebilir.<\/span><\/p>\n

\n\n
<\/div>\n\n<\/div>\n \n