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Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial

Vaidyanathan, P. P. (1990) Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial. Proceedings of the IEEE, 78 (1). pp. 56-93. ISSN 0018-9219. doi:10.1109/5.52200.

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Multirate digital filters and filter banks find application in communications, speech processing, image compression, antenna systems, analog voice privacy systems, and in the digital audio industry. During the last several years there has been substantial progress in multirate system research. This includes design of decimation and interpolation filters, analysis/synthesis filter banks (also called quadrature mirror filters, or QMFJ, and the development of new sampling theorems. First, the basic concepts and building blocks in multirate digital signal processing (DSPJ, including the digital polyphase representation, are reviewed. Next, recent progress as reported by several authors in this area is discussed. Several applications are described, including the following: subband coding of waveforms, voice privacy systems, integral and fractional sampling rate conversion (such as in digital audio), digital crossover networks, and multirate coding of narrow-band filter coefficients. The M-band QMF bank is discussed in considerable detail, including an analysis of various errors and imperfections. Recent techniques for perfect signal reconstruction in such systems are reviewed. The connection between QMF banks and other related topics, such as block digital filtering and periodically time-varying systems, based on a pseudo-circulant matrix framework, is covered. Unconventional applications of the polyphase concept are discussed.

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Vaidyanathan, P. P.0000-0003-3003-7042
Additional Information:© Copyright 1990 IEEE. Reprinted with permission. Manuscript received October 12, 1988; revised June l3, 1989.This work was supported in part by the National Science Foundation under grants DCI 8552579 and MIP 8604456. I would like to thank Dr. R. E. Crochiere of the AT&T Bell Labs for his encouragement in the preparation of this article. It is a privilege to acknowledge the useful discussions I have had with Dr. M. Bellanger of TRT, France, Prof. M. Vetterli of Columbia University, Profs. Smith and Barnwell of Georgia Institute of Technology, and Prof. T. Ramstad of the Norwegian Institute of Technology. Also, the input from reviewers resulted in useful improvements of this paper. Finally, the valuable “multirate interaction” I have had with my graduate students during the last few years is gratefully acknowledged. In particular, Zinnur Doğanata’s interactions on lossless systems, Vincent Liu’s interactions on nonuniform sampling and on 2D systems, and Truong Nguyen’s interactions on symmetric and linear-phase QMF banks have been particularly beneficial.
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