General multirate building structures with application to nonuniform filter banks

This paper proposes a general linear dual-rate structure for multirate signal processing, which encompasses the usual multirate building blocks-expanders, LTI filters, decimators, and their cascade combinations-as special cases. Structural properties of such dual-rate systems are studied in detail; in particular, several equivalent implementation structures are proposed: (1) cascade connections of a block expander, a linear periodically time-varying system, and a block decimator; (2) vector sample-rate changers; and (3) cascade connections of an expander, certain linear switching time-varying system, and a decimator. Using such general building blocks in multirate signal processing allows more design freedom and therefore can achieve what is otherwise impossible. This is illustrated in nonuniform multirate filter banks. Using the general building blocks as synthesis systems, the incompatibility for alias cancellation and structural dependency constraint for design, both due to fractional decimation ratios in different channels, are eliminated. Hence optimal design of synthesis systems is possible.

[1]  C. Barnes,et al.  Multirate recursive digital filters--A general approach and block structures , 1983 .

[2]  Mark J. T. Smith,et al.  Block decimated analysis-synthesis filter banks , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[3]  Thomas W. Parks,et al.  Linear periodic systems and multirate filter design , 1994, IEEE Trans. Signal Process..

[4]  P. Vaidyanathan,et al.  Non-uniform multirate filter banks: theory and design , 1989, IEEE International Symposium on Circuits and Systems,.

[5]  S. Mitra,et al.  Block implementation of recursive digital filters--New structures and properties , 1978 .

[6]  G. S. Moschytz,et al.  Block Implementation of Recursive Digital Filters-New Structures and Properties , 1978 .

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

[8]  Tongwen Chen,et al.  General multirate building blocks and their application in nonuniform filter banks , 1997, Proceedings of 1997 IEEE International Symposium on Circuits and Systems. Circuits and Systems in the Information Age ISCAS '97.

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

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

[11]  Tongwen Chen.  A lifting approach to analysis and design of nonuniform multirate filter banks , 1995, Proceedings 1995 Canadian Conference on Electrical and Computer Engineering.

[12]  G. David Forney,et al.  Convolutional codes I: Algebraic structure , 1970, IEEE Trans. Inf. Theory.

[13]  Xiang-Gen Xia,et al.  Multirate filter banks with block sampling , 1996, IEEE Trans. Signal Process..

[14]  Tongwen Chen,et al.  Design of multirate filter banks by /spl Hscr//sub /spl infin// optimization , 1995 .

[15]  R. G. Shenoy.  Multirate specifications via alias-component matrices , 1998 .

[16]  Sanjit K. Mitra,et al.  Polyphase networks, block digital filtering, LPTV systems, and alias-free QMF banks: a unified approach based on pseudocirculants , 1988, IEEE Trans. Acoust. Speech Signal Process..

[17]  Mark J. T. Smith,et al.  Time-varying analysis-synthesis systems based on filter banks and post filtering , 1995, IEEE Trans. Signal Process..

[18]  Alberto Leon-Garcia,et al.  Perfect reconstruction conditions for subband decomposition with generalized subsampling , 1992, Other Conferences.

[19]  D. Meyer.  A new class of shift-varying operators, their shift-invariant equivalents, and multirate digital systems , 1990 .

[20]  Xiang-Gen Xia,et al.  Vector-valued wavelets and vector filter banks , 1996, IEEE Trans. Signal Process..

[21]  Mark J. T. Smith,et al.  Nonuniform filter banks: a reconstruction and design theory , 1993, IEEE Trans. Signal Process..

[22]  C. Barnes,et al.  Block-shift invariance and block implementation of discrete-time filters , 1980 .

[23]  C. Sidney Burrus,et al.  A unified analysis of multirate and periodically time-varying digital filters , 1975 .

[24]  Truong Q. Nguyen,et al.  Wavelets and filter banks , 1996 .

[25]  Jelena Kovacevic,et al.  Perfect reconstruction filter banks with rational sampling factors , 1993, IEEE Trans. Signal Process..

[26]  Chia-Chuan Hsiao.  Polyphase filter matrix for rational sampling rate conversions , 1987, ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[27]  A. Leon-Garcia,et al.  Subband decomposition of signals with generalized sampling , 1993, IEEE Trans. Signal Process..

[28]  R.G. Shenoy.  Analysis of multirate components and application to multirate filter design , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[29]  Shahriar Mirabbasi,et al.  Controlling distortions in maximally decimated filter banks , 1997 .

[30]  R. Reng.  Polyphase and Modulation Descriptions of Multirate Systems - A Systematic Approach , 1995 .

[31]  David J. N. Limebeer,et al.  Linear Robust Control , 1994 .

[32]  Li Qiu,et al.  H∞ design of general multirate sampled-data control systems , 1994, Autom..

[33]  Tongwen Chen,et al.  Nonuniform multirate filter banks: analysis and design with an 𝒽∞ performance measure , 1997, IEEE Trans. Signal Process..

[34]  P. Strevens.  Iii , 1985 .