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Two-dimensional digital filters. (English) Zbl 0852.93001
Electrical Engineering and Electronics. 80. New York, NY: Marcel Dekker. xii, 398 p. (1992).
We have before us a solid book (398 pages) on two-dimensional (2-D) filters. To this subject many papers and some books have been devoted during the last two decades. The objective of this book is, as it is said in the preface, to provide basic theories, techniques and procedures for analysing, designing and implementing 2-D filters.
First, we give its Contents: Preface; Introduction; (1) Fundamentals; (2) State-space Methods; (3) Transform Methods; (4) The Application of the $$z$$-transform; (5) Stability Analysis; (6) Approximation for Nonrecursive Filters; (7) Approximation for Recursive Filters; (8) Design of Recursive Filters by Optimization; (9) Design of Nonrecursive Filters by Optimization; (10) Realization; (11) Finite Wordlength Effects; (12) Implementation; (13) Applications; Index.
The authors are significant researchers in the 2-D filter area: W.-S. Lu made some contributions in the 2-D stability theory while A. Antoniou is the author of a reference book on 1-D filters which is at its second edition. The book could be divided into three parts: a) fundamentals (1), (2), (3), (4), (5); b) approximation of (recursive and nonrecursive) filters (6), (7), (8), (9); c) ways to put the designed filters into operation (10), (11), (12). From the beginning, the authors emphasize the existence of four steps involved in the complete design of 2-D filters: approximation, realization, implementation, study of quantization effects. All these steps are discussed for each class of filters, this fact being the main merit of the book. Also we would remark some methodological aspects related to the book. As it is well known, the analysis of 2-D filters extensively uses the spate-space description. In opposition to the 1-D situation, in the 2-D case there are several ways to express the state-space equations. The authors choose to use the Givone-Roesser model which is more simple than others and is particularly suitable for the analysis of quantization effects. The second feature is the great attention paid to stability analysis. This stems from the fact that the rational transfer functions, which are the ratio of two polynomials in two complex variables $$z_1$$ and $$z_2$$, cannot be analysed with the tools of the 1-D case. In the 2-D case there may occur contours of zeros or of poles when the polynomials are not factorable, so that the fundamental theorem of algebra cannot be used. The merit (which is of crucial importance for a deep study) is in giving and quoting basic results and the papers where they are to be found. The numerous examples and (proposed) problems given at the end of each chapter provide a powerful tool insuring a deeper understanding of the theory given in the chapters. We think the book represents a remarkable reference text for students and engineers working in the area of 2-D filter theory and believe that it will do so for a long time.

##### MSC:
 93-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory 93C55 Discrete-time control/observation systems 93C62 Digital control/observation systems