Pencere Fonksiyonu Aileleri ve Uygulama Alanları

Yıl 2010, Cilt: 26 Sayı: 3, 291 - 306, 01.06.2010

Turgay Kaya Melih Cevdet İnce

Öz

Pencere fonksiyonları (veya kısaca pencere), sonlu impuls cevaplı (FIR, Finite Impulse Response) sayısal filtre tasarımında istenmeyen salınımları ortadan kaldırmak için kullanılan yapılardır. Pencere fonksiyonu analob genişliği, dalgalanma oranı ve yan lob azalma oranı gibi fonksiyonun performansını etkileyen parametrelere sahiptir. Bir pencere fonksiyonu tasarımında temel amaç, istenilen özellikleri sağlayacak genlik spektrumuna düşük derece ve en uygun spektral parametre değerleriyle ulaşmaktır. Bu çalışmanın amacı, pek çok uygulama alanında tercih edilen pencere fonksiyonu ailelerini belirlemek ve bu fonksiyonlar için yeni yaklaşımları incelemektir.

Anahtar Kelimeler

Pencere fonksiyonu ailesi, Kaiser penceresi, Ultraspherical pencere, FIR filtre

Window Function Families and Their Application Areas

Öz

Window functions (or shortly windows) are structures being used to eliminate undesired oscillations at FIR (Finite Impulse Response) digital filter design. Window function has parameters, which affect window performance, such as mainlobe width, ripple ratio and sidelobe roll-off ratio. The main aim at window function design is to reach amplitude spectrum providing desired properties with low degree and optimum spectral parameter values. The goal of this study is to determine window function families preferred at many application areas and to examine the new approaches for these functions.

Anahtar Kelimeler

Window function families, Kaiser window, Ultraspherical window, FIR filter

Kaynakça

• J.W. Gibbs, Fourier series, s. 200-606 (1899).
• L. Fejer, Sur les fonctions bornees et integrables, Comptes Rendus Hebdomadaries, Seances de l'Academie de Sciences, Paris, 131 984-987 (1900).
• C. Lanczos, Applied Analysis. Van Nostrand, Princeton, NJ. (1956).
• J.W. Adams, A new optimal window. IEEE Transactions on Signal Processing. 39 (8) (1991) 1753-1769.
• S.J. Mitra, Digital Signal Processsig A Computer-Based Approach, s-972, McGraw-Hill International Edition, (2006), Singapore.
• C.L. Dolph, A current distribution for broadside arrays which optimizes the relationship between beamwidth and side-lobe level, Proc. IRE, 34 335- 348 (1946) June.
• F.J. Harris, On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE. 66 51-83 (1978).
• J.F. Kaiser, Nonrecursive digital filter design using I0-sinh window function. Proc. IEEE Int. Symp. Circuits and Systems (ISCAS’74), San Francisco, Calif., USA, 20-23 (1974) April
• T. Saramaki, A class of window functions with nearly minimum sidelobe energy for designing FIR filters. Proc. IEEE Int. Symp. Circuits and systems (ISCAS’89), Portland, Ore, USA, 359- 362 (1989) May, 1.
• Nuttall, A. H., Some Windows with Very Good Sidelobe Behavior, IEEE Transactions on Acoustics, Speech, and Signal Processing, 29 (1) 84-91 (1981).
• A.G. Deczky, Unispherical Windows, IEEE Int. Symp. on Circuits and Systems. Sydney, Australia, May, 2 85-88 (2001).
• S.W.A. Bergen, A. Antoniou, Generation of Ultraspherical window functions, in XI European Signal Processing Conference, Toulouse, France, September, 2 607-610 (2002).
• Bergen, S.W.A., Antoniou, A., Design of Ultraspherical Window Functions with Prescribed Spectral Characteristics, EURASIP Journal on Applied Signal Processing, 13 2053- 2065 (2004).
• S.W.A. Bergen, A. Antoniou, Nonrecursive Digital Filter Design Using the Ultraspherical Window, IEEE Pacific Rim Conference On Communications, Computers, And Signal Processing, 260-263 (2003), August 28-30.
• Bergen, S.W.A. and Antoniou, A., Design of Nonrecursive Digital Filters Using the Ultraspherical Window Function, EURASIP Journal on Applied Signal Processing, 12 1910- 1922 (2005).
• K. Avci, A. Nacaroğlu., A new window based on exponential function, IEEE Ph.D. Research in Microelectronics and Electronics (PRIME 2008). June. Istanbul, Turkey, 69-72 (2008).
• K. Avci, A. Nacaroğlu., Kaiser Yaklaşımı Kullanılarak Oluşturulan Üstel Pencereyle Yinelemesiz Sayısal Süzgeç Tasarımı, Çukurova Üniversitesi Mühendislik –Mimarlık Fakültesi 30. Yıl Sempozyumu, Adana, 274-279 (2008) 16-17-Ekim.
• K. Avci, A. Nacaroğlu., High Quality Low Order Nonrecursive Digital Filter Design Using Modified Kaiser Window, Proc. of 6th Symposium on Communication Systems, Networks and Digital Signal processing (CSNDSP’08). July. Graz, Austria, 239-242 (2008).
• K. Avci, A. Nacaroğlu., Cosine hyperbolic window family with its application to FIR filter design. Proc. of Third International Conference on Information and Communication Technologies (ICTTA’08). April. Damascus, Syria, 289-290 (2008).
• Avci, K. and Nacaroğlu, A., Cosh window family and its application to FIR filter design, International Journal of Electronics and Communications-AEU, 63 906-917 (2009).
• K. Avci, A. Nacaroğlu, Modification of Cosh window family. Proc. of Third International Conference on Information and Communication Technologies (ICTTA’08), Damascus, Syria, 291-292 (2008), April.
• T. Kaya, M.C. İnce, The Calculation of Adjustable Window Parameters With Helping GA, Applied Automatic Systems (AAS’2009), Ohrid, Republic of Macedonia, 135-138 (2009) September 26-29.
• T. Kaya, M.C. İnce, Yüksek Performanslı Pencere Fonksiyonlarının Genetik Algoritma Yardımıyla Gerçekleştirilmesi, 3. Haberleşme Teknolojileri ve Uygulamaları Sempozyumu, (HABTEKUS’09) 235-238 (2009) 9-11 Aralık.
• T. Kaya, M.C. İnce, The FIR Filter Design By Using Window Parameters Calculated With GA, Soft Computing, Computing with Words and Perceptions in System Analysis, Decision and Control- (ICSCCW 2009), 1-4 (2009) September 2-4.
• T.S. Huang,Two-Dimensional Windows, IEEE Transactions on Audio and Electroacoustics, 88- 89 (1972) March.
• T. C. Speak, R.M. Mersereau, A Comparison of Different Window Formulations for Two- Dimensional FIR Filter Design, in IEEE Acoust., Speech, Signal Processing Conf. Rec., 5-8 (1979) April.
• T. C. Speak, R.M. Mersereau, A Note on the Use of Windows for Two-Dimensional FIR Filter Design, IEEE Trans. Acoust., Speech, Signal Processing, ASSSP-29, 125-128 (1981), August.
• J. H. McClellan, The design of two dimensional digital filters by transformation, in Proc. 7th Annu. Princeton Conf. Inform. Sci. Syst., 247- 251 (1973).
• Yu, T.H., Mitra, S. K., A New Two- Dimensional Window, IEEE Transaction on Acoustics, Speech, and Signal Processing., 33 (4) 1058- 1061 (1985).
• Lu, H. C., Yeh, K.H., Optimal design of 2-D FIR digital filters by scaling-free McClellan transformation using least-squares estimation, Signal Processing, 58 (1997) 303-308.
• Antoniou, A., Lu, W.S., Design of 2-D nonrecursive filters using of the window method, IEE Proceedings, 137 (4) 247- 250 (1990).
• Bernabo, F., Emiliani, P.L., Design of 2- dimensional recursive digital filters, Electronics Letters, 12 (11) 288-289 (1976) May-27.
• Hu, J. V., Rabiner, L. R., Design Techniques for Two Dimensional Digital Filters, IEEE Transaction on Audio and Electroacoustis, 20 (4) 249- 257 (1972).
• Charalmbous, C. Design of 2-dimensional circularly-symmetric digital filters, IEE Proceedings, 129 (2) 47-54 (1982).
• D. J. Shpak, A Transformation Method for the Design of Two-Dimensional Circularly- Symmetric FIR Digital Filters, IEEE International Symposium on Circuits and System, 2475-2478 (1991).
• Mladenov, V. M., Mastorakis, N. E., Design of Two-Dimensional Recursive Filters by Using Neural Networks, IEEE Transactions on Neural Networks, 12 (3) 585-560 (2001).
• Mastorakis, N. E., Gonos, L. F., Swamy, M.N.S., Design of Two-Dimensional Recursive Filters Using Genetic Algorithm, IEEE Transactions on Circuit and Systems-I: Fundamental Theory and Applications, 50 (5) 34-639 (2003).
• J.T. Tsai, J.H. Chou, T.K. Liu, C.H. Chen,  Design of Two-Dimensional Recursive Filters by Using a Navel Genetic Algorithm, IEEE International Symposium on Circuits and Systems (ISCAS-2005), 2603-2606 (2005).
• Tsai, J.T. Ho, W. H., Chou, J.H., Design of two- dimensional IIR digital structure-specified filters by using an improved genetic algorithm, Expert Systems with Applications, 36 6928- 6934 (2009).
• K. Avci, Design of High-Quality Low order Nonrecursive Digital Filters Using the Window Functions, PH. D. Thesis in University of Gaziantep, (2008) Gaziantep.
• W. S. Lu, A. Antoniou, Two-Dimensional Digital Filters, s.397, Marcel Dekker Inc. (1992) New York.