Signal processing and systems theory. Selected topics
type: Item
instance of: scholarly article
title: Signal processing and systems theory. Selected topics
zbMATH Open document ID: 0824.93002
author: Charles K. Chui
author: Guanrong Chen
published in: Springer Series in Information Sciences
publication date: 1994-04-20T00:00:00Z
review text: In the last twenty years, the interest for functions of a complex variable analytic in a half-plane decreased gradually (for applications). At the same time, the interest grew for functions of a complex variable analytic in the unit disk. This is so because the importance of discrete signals and systems whose complex frequency domain is the unit disk increased dramatically. Many results of mathematical origin concerning the behavior of complex functions on the unit disk became of great use and importance in recent applications. The book under consideration contains some topics from Discrete Signal Processing (DSP) and Discrete System Theory (DST) which are related to the theory of functions of a complex variable analytic in the unit disk. There are only six chapters in a volume of 268 p. Here are its contents: (1) Digital signals and digital filters; (2) Linear filters; (3) Approximation in Hardy spaces; (4) Optimal Hankel-norm approximation and \(H^ \infty\) minimization; (5) General theory of Hankel-norm approximation; (6) \(H^ \infty\) optimization and system reduction for MIMO systems, References, Further reading, List of symbols and a Subject index. The first two chapters provide standard results in a rigorous exposition. The fundamental concepts of linear systems (observability, minimal realization, sensitivity) for SISO (single input-single output) as well as for MIMO (multiple input-multiple output) systems are given. The chapter 3 gives an introduction to approximation in Hardy spaces. The celebrated Nevanlinna-Pick theorem and Pick's algorithm are discussed. Chapter 4, where Hankel-norm approximation and \(H^ \infty\) minimization are related by the famous AAK theorem (Adamjan, Arov and Krein), is important. By this connection, many facts belonging to operator theory can be translated into the language of DSP or DST. The book is written with great and beautiful rigor. It is accessible to mathematicians but is less accessible to engineers unless they like a…
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93B28
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93B36
Mathematics Subject Classification ID: 30D55
zbMATH DE Number: 555720
zbMATH Keywords: discrete system
zbMATH Keywords: digital signals
zbMATH Keywords: digital filters
zbMATH Keywords: approximation in Hardy spaces
zbMATH Keywords: optimal Hankel-norm approximation
zbMATH Keywords: \(H\)-\(\infty\) minimization
reviewed by: Dumitru Stanomir
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 555720