Conference Paper

# Design of Two-Channel Quadrature Mirror Filter Banks Using Differential Evolution with Global and Local Neighborhoods.

DOI: 10.1007/978-3-642-27172-4_1 Conference: Swarm, Evolutionary, and Memetic Computing - Second International Conference, SEMCCO 2011, Visakhapatnam, Andhra Pradesh, India, December 19-21, 2011, Proceedings, Part I

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**ABSTRACT:**The work of P. P. Vaidyanathan is an impressive text book aiming to present an in-depth study of multirate systems and filter banks. Multirate signal processing systems are systems containing beside multipliers, adders and delay elements, decimators and expanders (devices that reduce respectively increase the sampling rate by integers). The book is structured in 14 chapters and 5 appendices. After a detailed description of the content in Ch. 1, chapters 2 and 3 give a short review of fundamental principles concerning signals, systems and digital filtering. Ch. 4 covers the fundamental of multirate techniques in connection with various applications. Multivariate filter banks as well as the theoretical foundation for alias cancellation and error elimination are presented in Ch. 5. A deeper study of multirate filter banks and design techniques including those based on parameters matrices is made in Ch. 6 to 8. Chapters 9 to 12 cover special topics on multirate signal processing as follows: roundoff noise effects in Ch. 9, block filtering, periodically time-varying systems and sampling theorems in Ch. 10, wavelet transforms and multidimensional multirate systems in Ch. 11 and 12 respectively. An in-depth coverage of multivariable and lossless systems, necessary for a better understanding of the above topics is given in Ch. 13 and 14. In the appendices matrix theory, random processes and Mason’s rule are reviewed as well as spectral factorization and the effects of quantization for subband signals. Except for the need of some notions concerning sampling, Z transform and digital filters, the book is self contained. It is written in a very clear and didactic style. It has a lot of figures which help the reader to understand the text. Useful for class-room as well as for self study (each chapter is supplemented with home-work problems) the book can help the reader not only to understand the topics but also to be able to start research in the domain of multirate filters. Vaidyanathan’s book is a most welcome addition to the literature on digital filtering.01/1993; Prentice-Hall. -
##### Conference Paper: A filter family designed for use in quadrature mirror filter banks

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**ABSTRACT:**This paper discusses a family of filters that have been designed for Quadrature Mirror Filter (QMF) Banks. These filters provide a significant improvement over conventional optimal equiripple and window designs when used in QMF banks. The performance criterion for these filters differ from those usually used for filter design in a way which makes the usual filter design techniques difficult to apply. Two filters are actually designed simultaneously, with constraints on the stop band rejection, transition band width, and pass and transition band performance of the QMF filter structure made from those filters. Unlike most filter design problems, the behavior of the transition band is constrained, which places unusual requirements on the design algorithm. The requirement that the overall passband behavior of the QMF bank be constrained (which is a function of the passband and stop band behavior of the filter) also places very unusual requirements on the filter design. The filters were designed using a Hooke and Jeaves optimization routine with a Hanning window prototype. Theoretical results suggest that exactly flat frequency designs cannot be created for filter lengths greater than 2, however, using the discussed procedure, one can obtain QMF banks with as little as ±.0015dB ripple in their frequency response. Due to the nature of QMF filter applications, a small set of filters can be derived which will fit most applications.Acoustics, Speech, and Signal Processing, IEEE International Conference on ICASSP '80.; 05/1980 - [Show abstract] [Hide abstract]

**ABSTRACT:**This work presents a method for the design of quadrature mirror filters. A new frequency weighted stopband energy function is introduced, which leads to considerable flexibility in the design process. Unlike other techniques which involve searches and nonlinear optimization, our formulation reduces the design equations to an eigenvector problem. Furthermore, the resulting filters are regular and have additional desirable properties for applications to pyramidal coding of images, which together with DPCM, PCM, vector quantization, or zero-tree wavelet coding schemes leads to high compression ratiosIEEE Transactions on Circuits and Systems II Analog and Digital Signal Processing 10/1997;

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