Multirate Systems and Filter Banks

The outline of this chapter is as follows. Section 2 reviews various types of existing finite impulse response (FIR) and infinite impulse response (IIR) two-channel filter banks. The basic operations of these filter banks are considered and the requirements are stated for alias-free, perfect-reconstruction (PR), and nearly perfect-reconstruction (NPR) filter banks. Also some efficient synthesis techniques are referred to. Furthermore, examples are included to compare various two-channel filter banks with each other. Section 3 concentrates on the design of multi-channel (M-channel) uniform filter banks. The main emphasis is laid on designing these banks using tree-structured filter banks with the aid of two-channel filter banks and on generating the overall bank with the aid of a single prototype filter and a proper cosine-modulation or MDFT technique. In Section 4, it is shown how octave filter banks can be generated using a single two-channel filter bank as the basic building block. Also, the relations between the frequency-selective octave filter banks and discrete-time wavelet banks are briefly discussed. Finally, concluding remarks are given in Section 5.

[1]  Tapio Saramäki,et al.  An iterative method for designing orthogonal two-channel FIR filter banks with regularities , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[2]  S. Biyiksiz,et al.  Multirate digital signal processing , 1985, Proceedings of the IEEE.

[3]  Martin Vetterli,et al.  Wavelets and filter banks: theory and design , 1992, IEEE Trans. Signal Process..

[4]  Charng-Kann Chen,et al.  Design of quadrature mirror filters with linear phase in the frequency domain , 1992 .

[5]  Xi Zhang,et al.  Design of QMF banks using allpass filters , 1995 .

[6]  Truong Q. Nguyen.  A quadratic-constrained least-squares approach to the design of digital filter banks , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[7]  Fred Mintzer,et al.  Filters for distortion-free two-band multirate filter banks , 1985, IEEE Trans. Acoust. Speech Signal Process..

[8]  T. Saramaki,et al.  Recursive Nth-band digital filters- Part I: Design and properties , 1987 .

[9]  David B. H. Tay,et al.  Design of causal stable IIR perfect reconstruction filter banks using transformation of variables , 1998 .

[10]  P. P. Vaidyanathan,et al.  A new class of two-channel biorthogonal filter banks and wavelet bases , 1995, IEEE Trans. Signal Process..

[11]  P. P. Vaidyanathan,et al.  Lattice structures for optimal design and robust implementation of two-channel perfect-reconstruction QMF banks , 1988, IEEE Trans. Acoust. Speech Signal Process..

[12]  T. Ramstad,et al.  Cosine-modulated analysis-synthesis filterbank with critical sampling and perfect reconstruction , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[13]  Henrique S. Malvar.  Extended lapped transforms: properties, applications, and fast algorithms , 1992, IEEE Trans. Signal Process..

[14]  O. Herrmann,et al.  Design of nonrecursive digital filters with minimum phase , 1970 .

[15]  Mark J. T. Smith,et al.  Time-domain filter bank analysis: a new design theory , 1992, IEEE Trans. Signal Process..

[16]  Shing-Chow Chan,et al.  Theory and design of causal stable IIR PR cosine-modulated filter banks , 1999, ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349).

[17]  Truong Q. Nguyen,et al.  Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters , 1989, IEEE Trans. Acoust. Speech Signal Process..

[18]  Yong Ching Lim,et al.  An efficient algorithm to design weighted minimax perfect reconstruction quadrature mirror filter banks , 1999, IEEE Trans. Signal Process..

[19]  Toshiro Homma.  On an Iterative Method , 1964 .

[20]  Mathukumalli Vidyasagar,et al.  New algorithms for constrained minimax optimization , 1977, Math. Program..

[21]  Mark J. T. Smith,et al.  A new algorithm for efficient low delay filter bank design , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[22]  Toshinori Yoshikawa,et al.  Design of two-channel IIR linear phase PR filter banks , 1999, Signal Process..

[23]  Andreas Antoniou,et al.  Efficient iterative design method for cosine-modulated QMF banks , 1996, IEEE Trans. Signal Process..

[24]  P. P. Vaidyanathan,et al.  Cosine-modulated FIR filter banks satisfying perfect reconstruction , 1992, IEEE Trans. Signal Process..

[25]  Tapio Saramäki,et al.  An efficient approach for designing nearly perfect-reconstruction low-delay cosine-modulated filter banks , 2002, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353).

[26]  P. P. Vaidyanathan,et al.  New results on cosine-modulated FIR filter banks satisfying perfect reconstruction , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[27]  P. Vaidyanathan.  Multirate Systems And Filter Banks , 1992 .

[28]  Sanjit K. Mitra,et al.  A simple method for designing high-quality prototype filters for M-band pseudo QMF banks , 1995, IEEE Trans. Signal Process..

[29]  Mark J. T. Smith,et al.  Exact reconstruction techniques for tree-structured subband coders , 1986, IEEE Trans. Acoust. Speech Signal Process..

[30]  Henrique S. Malvar,et al.  Signal processing with lapped transforms , 1992 .

[31]  Tapio Saramäki,et al.  A general-purpose optimization technique for designing two-channel FIR filter banks , 2000, 2000 10th European Signal Processing Conference.

[32]  O. Herrmann.  On the approximation problem in nonrecursive digital filter design , 1971 .

[33]  Gerald Schuller,et al.  Modulated filter banks with arbitrary system delay: efficient implementations and the time-varying case , 2000, IEEE Trans. Signal Process..

[34]  Bin-Chang Chieu,et al.  Perfect-reconstruction filter banks having linear-phase FIR filters with equiripple response , 1998, IEEE Trans. Signal Process..

[35]  Sanjit K. Mitra,et al.  A novel implementation of perfect reconstruction QMF banks using IIR filters for infinite length signals , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[36]  Tanja Karp,et al.  Computationally efficient realization of MDFT filter banks , 1996, 1996 8th European Signal Processing Conference (EUSIPCO 1996).

[37]  Jelena Kovacevic,et al.  Wavelets and Subband Coding , 2013, Prentice Hall Signal Processing Series.

[38]  Toshinori Yoshikawa,et al.  Design of causal IIR perfect reconstruction filter banks , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[39]  E. D. Re,et al.  Design of biorthogonal M-channel cosine-modulated FIR/IIR filter banks , 2000, IEEE Trans. Signal Process..

[40]  Mark J. T. Smith,et al.  New framework for modulated perfect reconstruction filter banks , 1996, IEEE Trans. Signal Process..

[41]  Shing-Chow Chan,et al.  Design of two-channel PR FIR filter banks with low system delay , 2000, 2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353).

[42]  Truong Q. Nguyen.  A class of generalized cosine-modulated filter bank , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[43]  Gerald Schuller.  Time-varying filter banks with variable system delay , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[44]  Truong Q. Nguyen.  Digital filter bank design quadratic-constrained formulation , 1995, IEEE Trans. Signal Process..

[45]  Tapio Saramäki,et al.  A systematic technique for designing prototype filters for perfect reconstruction cosine modulated and modified DFT filter banks , 2001, ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196).

[46]  Tanja Karp,et al.  Modified DFT filter banks with perfect reconstruction , 1999 .

[47]  B.-R. Horng,et al.  Lagrange multiplier approaches to the design of two-channel perfect-reconstruction linear-phase FIR filter banks , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[48]  S.C. Chan,et al.  A new design method for two-channel perfect reconstruction IIR filter banks , 2000, IEEE Signal Processing Letters.

[49]  Andreas Antoniou,et al.  A new method for the design of FIR quadrature mirror-image filter banks , 1998 .

[50]  I. Daubechies,et al.  Factoring wavelet transforms into lifting steps , 1998 .

[51]  N. J. Fliege,et al.  Computational efficiency of modified DFT polyphase filter banks , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[52]  R. Ansari,et al.  FIR/IIR exact reconstruction filter banks with applications to subband coding of images , 1991, [1991] Proceedings of the 34th Midwest Symposium on Circuits and Systems.

[53]  Chen-Huei Chiang,et al.  Wavelets and perfect reconstruction subband coding with causal stable IIR filters , 1995 .

[54]  Yong Ching Lim,et al.  The design of weighted minimax quadrature mirror filters , 1993, IEEE Trans. Signal Process..

[55]  Andreas Antoniou,et al.  Design of low-delay two-channel FIR filter banks using constrained optimization , 1996, Signal Process..

[56]  T. Saramaki,et al.  Design of causal stable perfect reconstruction two-channel IIR filter banks , 2001, ISPA 2001. Proceedings of the 2nd International Symposium on Image and Signal Processing and Analysis. In conjunction with 23rd International Conference on Information Technology Interfaces (IEEE Cat..

[57]  Truong Q. Nguyen,et al.  The theory and design of arbitrary-length cosine-modulated filter banks and wavelets, satisfying perfect reconstruction , 1996, IEEE Trans. Signal Process..

[58]  Truong Q. Nguyen.  Near-perfect-reconstruction pseudo-QMF banks , 1994, IEEE Trans. Signal Process..

[59]  Truong Q. Nguyen,et al.  A general formulation of modulated filter banks , 1999, IEEE Trans. Signal Process..

[60]  Henrique S. Malvar.  Extended lapped transforms: fast algorithms and applications , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[61]  W. Sweldens.  The Lifting Scheme: A Custom - Design Construction of Biorthogonal Wavelets "Industrial Mathematics , 1996 .

[62]  Tapio Saramiiki.  Designing Prototype Filters for Perfect- Reconstruction Cosine-Modulated Filter Banks , 1992 .

[63]  Chun Sum Ng,et al.  Improved weighted least squares algorithm for the design of quadrature mirror filters , 1999, IEEE Trans. Signal Process..

[64]  Joseph Rothweiler,et al.  Polyphase quadrature filters-A new subband coding technique , 1983, ICASSP.

[65]  Henrique S. Malvar.  Modulated QMF filter banks with perfect reconstruction , 1990 .

[66]  Jean-Michel Poggi,et al.  Wavelet Toolbox User s Guide , 1996 .

[67]  L. Rabiner,et al.  A computer program for designing optimum FIR linear phase digital filters , 1973 .

[68]  D. Esteban,et al.  Application of quadrature mirror filters to split band voice coding schemes , 1977 .

[69]  Masahiro Okuda,et al.  Image coding using wavelets based on two-channel linear phase orthogonal IIR filter banks , 1999, Proceedings 1999 International Conference on Image Processing (Cat. 99CH36348).

[70]  Lajos Gazsi,et al.  Explicit formulas for lattice wave digital filters , 1985 .

[71]  Alfred Mertins,et al.  Efficient biorthogonal cosine-modulated filter banks , 2001, Signal Process..

[72]  T. Ramstad.  IIR filterbank for subband coding of images , 1988, 1988., IEEE International Symposium on Circuits and Systems.

[73]  Andreas Antoniou,et al.  An improved method for the design of FIR quadrature mirror-image filter banks , 1998, IEEE Trans. Signal Process..

[74]  Tapio Saramäki,et al.  An efficient approach for designing nearly perfect-reconstruction cosine-modulated and modified DFT filter banks , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[75]  Thierry Blu,et al.  A new design algorithm for two-band orthonormal rational filter banks and orthonormal rational wavelets , 1998, IEEE Trans. Signal Process..

[76]  James D. Johnston,et al.  A filter family designed for use in quadrature mirror filter banks , 1980, ICASSP.

[77]  Truong Q. Nguyen,et al.  Improved technique for design of perfect reconstruction FIR QMF banks with lossless polyphase matrices , 1989, IEEE Trans. Acoust. Speech Signal Process..

[78]  Alfred Mertins,et al.  Lifting schemes for biorthogonal modulated filter banks , 1997, Proceedings of 13th International Conference on Digital Signal Processing.

[79]  W. Wegener,et al.  Wave digital directional filters with reduced number of multipliers and adders , 1979 .

[80]  Mark J. T. Smith,et al.  Low delay FIR filter banks: design and evaluation , 1994, IEEE Trans. Signal Process..