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      Çok-bileşenli sinyallerin analizi için destek bölge uyarlamalı hermite-gauss açılımı

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      Author
      Alp, Yaşar Kemal
      Arıkan, Orhan
      Özertem, U.
      Date
      2011-04
      Source Title
      IEEE 19th Signal Processing and Communications Applications Conference, SIU 2011
      Publisher
      IEEE
      Pages
      430 - 433
      Language
      Turkish
      Type
      Conference Paper
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      Abstract
      Zaman-frekans destek bölgesi orijin etrafında dairesel bir alana uyan bir sinyal bileşeni için, Hermite-Gauss açılımı en az sayıda taban fonsiyonu kullanarak en iyi temsili oluşturur. Ancak, orijinden uzakta ve dairesel olmayan zaman-frekans destek noklarına sahip sinyal bileşenleri için Hermite-Gauss açılımının direk uygulanması, çok fazla sayıda Hermite-Gauss fonksiyonunun kullanımını gerektirir. Bu da, eğer ölçüm sinyali gürültü altında kaydedilmişse ya da birçok sinyal bileşeni içeriyorsa, başarısız bileşen kestirimlerine neden olur. Bu problemi çözmek için sinyal bileşenlerinin destek bölgelerini bulup, zaman-frekans düzleminde orijin civarında, dairesel bir bölgeye oturtan ve bu sayede en az sayıda Hermite-Gauss fonksiyonu kullanarak sinyal bileşenlerini başarılı bir şekilde kestiren, tamamen otomatikleştirilmiş bir önişleme yöntemi önermekteyiz. Önişlemenin ardından, kestirilen bileşenlere ters dönüşümler uygulanarak destek bölgeleri eski yerlerine taşınır
       
      For a signal component whose time-frequency support tightly fits into a circular region around origin, Hermite-Gaussian function expansion provides optimal representation by using the fewest number of basis functions. However, for signal components which have non-circular time-frequency supports away from the origin, straight forward expansions require excessively large number of Hermite-Gaussians which result in unreliable component estimates especially when the available observation is noisy or includes multiple components. To alleviate this problem, we propose a fully automated pre-processing technique which identifies and transforms supports of individual signal components to a circular region centered around origin so that the fewest number of Hermite-Gaussians can be used for obtaining reliable component estimates. Then, estimated components are post-processed to transform their supports back to their original positions. © 2011 IEEE.
      Keywords
      Basis functions
      Circular region
      Hermite-Gaussian function
      Multicomponent signals
      Multiple components
      Non-circular
      Pre-processing
      Reliable components
      Signal components
      Time frequency
      Expansion
      Signal processing
      Gaussian distribution
      Permalink
      http://hdl.handle.net/11693/28391
      Published Version (Please cite this version)
      http://dx.doi.org/10.1109/SIU.2011.5929679
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      • Department of Electrical and Electronics Engineering 3524
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