## Multirate systems and filter banks.(English)Zbl 0784.93096

Prentice Hall Signal Processing Series. Englewood Cliffs, NJ: PTR Prentice Hall. xvi, 911 p. (1993).
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.
Reviewer: L.Goras (Iaşi)

### MSC:

 93E11 Filtering in stochastic control theory 93-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory 93B51 Design techniques (robust design, computer-aided design, etc.) 94A12 Signal theory (characterization, reconstruction, filtering, etc.)