İki-boyutlu Kompleks İşaretlerin Yüksek Çözünürlüklü Spektrum Kestirimi
İki-boyutlu Kompleks İşaretlerin Yüksek Çözünürlüklü Spektrum Kestirimi
Dosyalar
Tarih
2009-06-12
Yazarlar
Kılınç, Umut Erdem
Süreli Yayın başlığı
Süreli Yayın ISSN
Cilt Başlığı
Yayınevi
Fen Bilimleri Enstitüsü
Institute of Science and Technology
Institute of Science and Technology
Özet
Bu çalışmada, iki-boyutlu (2-B) kompleks işaretlerin yüksek çözünürlüklü spektrum kestirim analizleri yapılmıştır. Bu amaçla 2-B kompleks işaret yapay olarak üretilerek üzerine gürültü işareti eklenmiş ve daha sonra farklı spektrum kestirim yöntemleri kullanılarak bu işarete ait frekans bileşenleri yüksek çözünürlük ve doğrulukla ortaya çıkarılmıştır. 2-B işaretin frekans bileşenlerinin bulunmasında iki çeyrek-düzlem (ÇD) destek bölgeleri, çoklu ÇD destek bölgeleri ve 2-B MUSIC algoritmaları kullanılmıştır. İki ÇD destek bölgeleri algoritmasında, 1. ve 2. ÇD destek bölgeleri için ayrı işaret spektrumları hesaplanmış ve bu spektrumların harmonik ortalamalarının alınmasıyla asıl spektrum kestirimi elde edilmiştir. Çoklu ÇD destek bölgeleri algoritması 2-B doğrusal kestirim yöntemini kullanmakla birlikte, standart ÇD destek bölgesinden türetilen yeni destek bölgelerinin kullanılması temeline dayanmaktadır. Her bir destek bölgesi için spektrum kestirimi farklı olup, bu kestirimlerin birleştirilmesiyle istenen sonuç spektrum kestirimi elde edilmiştir. 2-B MUSIC algoritması, işaretin özilinti matrisinin işaret ve gürültü alt uzaylarına ayrışımı ve özilinti matrisinin özvektörlerinden yararlanılması temeline dayanmaktadır. Kullanılan yöntemlerin her biri uygulama programları ile gerçeklenerek elde edilen sonuçlar farklı işaret parametreleri için karşılaştırılmıştır. Ayrıca, 2-B işaretin spektrum kestiriminde önemli rol oynayan özilinti matrisinin kestirim yöntemleri ve bu kestirimlerin 2-B spektrum kestirimine olan etkisi incelenerek farklı işaret örnek değerlerinde spektrum kestirimi için en uygun özilinti kestirim yöntemleri önerilmiştir.
In this thesis, the high-resolution spectrum estimation analysis of two-dimensional (2-D) complex signals was performed. For this purpose, a synthetic 2-D complex signal model was created; the noise signal was added on it and so on various 2-D spectrum estimation methods were applied to obtain the frequency contents of the signal with high resolution and accuracy. In order to extract the frequency contents of the 2-D signal, two Quarter-Plane (QP) regions of support, multiple QP regions of support and 2-D MUSIC algorithms were applied. In two QP region of support algorithm, the spectrums for the first and second standard QP regions of support were obtained and after combining and taking the harmonic mean of these spectrums, the exact spectrum of 2-D signal was acquired. Multiple QP regions of support algorithm is based on 2-D linear prediction models with new regions of support extracted from standard quarter plane support region. Since each support region creates various signal spectrums, these separate spectrums are combined and the final spectrum estimation is obtained. 2-D MUSIC algorithm is based on the idea that the autocorrelation matrix of 2-D signal is eigendecomposed to signal and noise subspaces and the method is benefited from eigenvectors of the autocorrelation matrix. These methods were realized with the application programs and the results obtained from each method were compared. In addition, the estimation methods of autocorrelation matrix which plays a major role at 2-D spectrum estimation is investigated and by showing the effects of estimation methods on 2-D spectrum, the most appropriate method is proposed for different signal sample values.
In this thesis, the high-resolution spectrum estimation analysis of two-dimensional (2-D) complex signals was performed. For this purpose, a synthetic 2-D complex signal model was created; the noise signal was added on it and so on various 2-D spectrum estimation methods were applied to obtain the frequency contents of the signal with high resolution and accuracy. In order to extract the frequency contents of the 2-D signal, two Quarter-Plane (QP) regions of support, multiple QP regions of support and 2-D MUSIC algorithms were applied. In two QP region of support algorithm, the spectrums for the first and second standard QP regions of support were obtained and after combining and taking the harmonic mean of these spectrums, the exact spectrum of 2-D signal was acquired. Multiple QP regions of support algorithm is based on 2-D linear prediction models with new regions of support extracted from standard quarter plane support region. Since each support region creates various signal spectrums, these separate spectrums are combined and the final spectrum estimation is obtained. 2-D MUSIC algorithm is based on the idea that the autocorrelation matrix of 2-D signal is eigendecomposed to signal and noise subspaces and the method is benefited from eigenvectors of the autocorrelation matrix. These methods were realized with the application programs and the results obtained from each method were compared. In addition, the estimation methods of autocorrelation matrix which plays a major role at 2-D spectrum estimation is investigated and by showing the effects of estimation methods on 2-D spectrum, the most appropriate method is proposed for different signal sample values.
Açıklama
Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2009
Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2009
Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2009
Anahtar kelimeler
Spektrum,
Destek Bölgesi,
Özilinti,
Spectrum,
Region of Support,
Autocorrelation