Reel ve kompleks sinüsoidallerin hızlı frekans kestirimi
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Date
2023-02-16
Authors
Bayazit, Hasan
Journal Title
Journal ISSN
Volume Title
Publisher
Bursa Uludağ Üniversitesi
Abstract
Gürültü içeren sinyallerin temel frekansının doğru bir şekilde kestirimi problemi uzun yıllardan beri üzerinde çalışılan bir konudur. Frekans kestirimi, ses, müzik, sismik, radar, sonar, medikal, mekanik, görüntü işleme ve güç sistemlerde sinyalin belirlenebilmesi, işlenebilmesi için yaygın olarak kullanılmaktadır. Frekans kestirimi konusunda oldukça fazla sayıda algoritmalar geliştirilmiştir. Ancak, ayrık Fourier dönüşümün (AFD) üç örneğini kullanan, sinc fonksiyonu interpolasyonuna dayanan hızlı frekans kestiriciler konusunda yapılan çalışmaların detay içermediği görülmüştür. Bu tezde, AFD dönüşümüne dayanan frekans kestirim yöntemi ve bu yöntemin uygulanmasında karşılaşılan sorunlar ve çözüm yolları detaylı bir şekilde açıklanmıştır. Reel ve kompleks sinyallerin ayrık Fourier dönüşümüne dayanan modelinden yola çıkarak, sinc interpolasyonuna dayanan üç farklı frekans kestiricisi önerilmiştir. Reel sinyallerin AFD genlik değerlerinin bin frekanslarına göre değişimi etraflıca açıklanmıştır. Kompleks sinyallerin AFD kompleks değerlerinin detaylı analizi sonucunda önerilen sinc frekans kestiricilerin belirlenmesinde kullanılabilecek özgün karar kriteri önerilmiştir. Önerilen frekans kestiricileri, parabolik, Jacobsen, yanlılığı iyileştirilmiş Jacobsen, Quinn frekans kestiricileriyle reel ve kompleks sinyaller için farklı örnek sayıları ve farklı sinyal-gürültü oranları için karşılaştırmaları yapılmıştır. Dijital sinyal işleme uygulamalarında hızlı ve doğru frekans kestirimi yapmasıyla ünlenmiş Jacobsen frekans kestiricisiyle birlikte kullanılabilecek bir yöntem önerilmiştir. Bu yöntem sayesinde, önerilen frekans kestiricilerin frekans spektrumunun geniş bir aralığında daha iyi performans gösterdikleri gözlenmiştir. Bu çalışma, sinc interpolasyonuna dayanan frekans kestirimi konusunda detaylı bir temel oluşturmaktadır. Geliştirilen frekans kestiriciler, karar verme kriteri ve önerilen metod, uluslararası yapılan çalışmalarla kıyaslandığında özgünlük taşıdığı değerlendirilmektedir.
The problem of accurately estimating fundamental frequency of the signals containing noise is a problem that has been studied for many years. Frequency estimation is widely used in sound, music, seismic, radar, sonar, medical, mechanical, image processing, and power systems for signal identification and processing. A large number of algorithms have been developed for frequency estimation. However, the studies on fast frequency estimators based on sinc function interpolation using three examples of discrete Fourier transform did not contain details. In this thesis, the frequency estimation method based on DFT transformation and the problems and solutions encountered in the application of this method are explained in detail. Three different sinc-based frequency estimators have been proposed based on the discrete Fourier transform model of real and complex signals. The variation of DFT amplitude values of a real signal according to bin frequencies is explained in detail. As a result of the detailed analysis of the DFT complex values of the complex signals, the original decision criterion to be used in the determination of the proposed sinc frequency estimators has been proposed. Comparisons of the proposed frequency estimators, parabolic, Jacobsen, biased Jacobsen, and Quinn frequency estimators for real and complex signals, for different sample numbers and different signal-to-noise ratios, were made. A method that can be used with the Jacobsen frequency estimator, famous for its fast and accurate frequency estimation in digital signal processing applications, is proposed. Thanks to this method, it has been observed that the proposed frequency estimators perform better in a wide range of the frequency spectrum. This study provides a detailed basis for frequency estimation based on sinc interpolation. The developed frequency estimators, the decision criteria, and the proposed method are considered original compared with international studies.
The problem of accurately estimating fundamental frequency of the signals containing noise is a problem that has been studied for many years. Frequency estimation is widely used in sound, music, seismic, radar, sonar, medical, mechanical, image processing, and power systems for signal identification and processing. A large number of algorithms have been developed for frequency estimation. However, the studies on fast frequency estimators based on sinc function interpolation using three examples of discrete Fourier transform did not contain details. In this thesis, the frequency estimation method based on DFT transformation and the problems and solutions encountered in the application of this method are explained in detail. Three different sinc-based frequency estimators have been proposed based on the discrete Fourier transform model of real and complex signals. The variation of DFT amplitude values of a real signal according to bin frequencies is explained in detail. As a result of the detailed analysis of the DFT complex values of the complex signals, the original decision criterion to be used in the determination of the proposed sinc frequency estimators has been proposed. Comparisons of the proposed frequency estimators, parabolic, Jacobsen, biased Jacobsen, and Quinn frequency estimators for real and complex signals, for different sample numbers and different signal-to-noise ratios, were made. A method that can be used with the Jacobsen frequency estimator, famous for its fast and accurate frequency estimation in digital signal processing applications, is proposed. Thanks to this method, it has been observed that the proposed frequency estimators perform better in a wide range of the frequency spectrum. This study provides a detailed basis for frequency estimation based on sinc interpolation. The developed frequency estimators, the decision criteria, and the proposed method are considered original compared with international studies.
Description
Keywords
Hızlı frekans kestirimi, Ayrık fourier dönüşümü, Sinc interpolasyon, Pencere fonksiyonları, Reel sinyal, Kompleks sinyal, Fast frequency estimation, DFT, Sinc interpolation, Window functions, Real signals, Complex signals
Citation
Bayazit, H. (2023). Reel ve kompleks sinüsoidallerin hızlı frekans kestirimi. Yayınlanmamış doktora tezi. Bursa Uludağ Üniversitesi Fen Bilimleri Enstitüsü.