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Reviewer: Vladimir Botchev

Vaidyanathan has written a successor to Multirate digital signal processing [1], which is not to say that the older book must be entirely replaced by this new one. The book could be regarded as an encyclopedia of multirate signal processing. Though expensive, the book is worth its price for the 900 pages of high-quality scientific and engineering information. It consists of four parts, divided into 14 chapters and five appendices, followed by a glossary, lists of figures and tables, and a bibliography. Part 1 is an introduction to general digital signal processing (DSP) as well as multirate systems, although at least an intermediate-level knowledge of DSP is needed to get the most out of the text. A brief introductory chapter presents some history of multirate processing. A review chapter on discrete time systems follows. Although brief, this chapter is dense and outlines many topics, including some advanced topics such as wrapped phase. Chapter 3 reviews digital filters with an introduction, coverage of major topics, and design examples. The author emphasizes all-pass filters. Chapter 4 introduces multirate systems. Here the reader can stop and try some practical implementations before continuing to the more sophisticated material in the next part, which deals with multirate filter banks. The topics in this part are maximally decimated filter banks (QMF filters and their M-channel extensions); para-unitary perfect reconstruction filter banks, which are useful both practically and as a first approach to wavelet analysis; and linear phase perfect reconstruction QMF banks and cosine modulated filter banks, which are attractive from a design standpoint and because fast implementation techniques can be used. Part 3 is of great interest because it discusses many nontrivial or new topics. The beginning chapter, on quantization effects, reviews effects in regular digital filters, and continues with the peculiarities of multirate systems. Chapter 1 0 addresses such topics as linear periodically time-varying systems and nonuniform sampling and their relations with multirate filter bank theory. It is hard to find a more comprehensive engineering introduction to the wavelet transform than chapter 12. The only competition is perhaps Malvar [2]. The approach is classical—Fourier transform, short-time Fourier transform, and time frequency representations lead naturally to the wavelet decomposition. This chapter is excellent, providing a strong theoretical basis and practical skills via the end-of-chapter exercises. The next chapter deals with multidimensional multirate systems. This chapter is highly complex, and although an introduction is provided, a background in the field, which Dudgeon and Mersereau [3] provides, would prove helpful. The last part discusses multivariate and lossless systems. The first chapter of this part reviews discrete time multi-input/multi-output LTI systems. It is mostly theoretical, and interested readers will find it useful, since it complements the discussions up to this point. While the topics in this part are classically part of control theory, readers can benefit greatly from them. Part 4 concludes with chapter 14, on para-unitary and lossless systems. The needed background is found in chapter 6. Appendix A reviews matrix manipulation, Appendix B reviews random processes, Appendices C and D cover quantization of subband signals and spectral factorization, and Appendix E reviews signal flowgraphs and gives Mason's gain formula. Exercises are provided in the appendices as well. If digital signal processing is your preferred activity, this book should be placed next to the Bible.