Digital Filters: Basics and Design

International Journal of Electrical Engineering Education,  Oct 2001  by Leeson, Mark

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D. Schlichtharle, Digital Filters: Basics and Design, Springer, 2000, 361 pp., L34; $54.95.

This is a very timely volume given the ever-increasing use of digital signal processing in modern devices such as mobile telephones, digital television and digital audio. It can be considered as two portions; chapters one to five (approximately one third of the book) are relatively brief and review the background necessary for the study of digital filters. In contrast, the remaining chapters (six to nine) constitute a more detailed treatment of material that is either advanced or necessary for practical filter realisation. The level is early postgraduate or advanced undergraduate but the book is not designed as a course text so does not offer problems and solutions at the end of each chapter.

The first chapter is a very brief review of the fundamentals of transforms and transfer functions for continuous time systems. This is followed by a second, longer, chapter that develops in a concise manner the theory of analogue filters from ideal lowpass to classic practical designs, such as Butterworth and Chebyshev. To round off the chapter, highpass, bandpass and bandstop filters are obtained from the lowpass case by means of transformations of the frequency variable.

Chapter three lays the foundations for discrete time analysis, covering the z-transform and discrete convolution. This leads naturally to the fourth chapter discussing the link between the continuous and discrete domains, namely sampling. Overviews of the theoretical background, with the appropriate mathematical analysis, and also the practical aspects are given.

The structure of digital filters is introduced in chapter five, beginning with FIR filters after a short preamble. Direct form IIR filters are then presented followed by a short general discussion of stability and minimum phase filters. Subsequently the idea of state space structures permits the development of the IIR normal form. The final sections of the chapter develop wave filters, concentrating on the lowpass case since a full coverage of this topic would considerably lengthen the book.

Chapters six and seven are concerned with the design of IIR and FIR filters, which require very different design techniques. The former are discussed first and their relationship to continuous time filters examined leading to a description of methods for design in both the time and the frequency domains. The chapter concludes with some examples of filter design given definite requirements, such as a prescribed time delay. The approach required for FIR design is then covered in the seventh chapter, which describes the use of frequency sampling, mean square error minimisation and Chebyshev approximation. In each case examples are used to demonstrate the strengths and weaknesses of the filters resulting from these procedures.

It is the eighth chapter that distinguishes this book from a standard undergraduate text as it goes far beyond what is necessary to understand and design a filter under examination conditions. All real filters must take account of the finite precision available to represent their coefficients. The importance of this fact to filters, and hence modern life, warrants the inclusion of a chapter that forms in excess of 20% of the book. After a review of number representation, quantisation is introduced leading to discussion of noise performance and its optimisation with the constraint of finite word lengths. Next there is an interesting discussion of the effect of finite coefficient wordlength on poles and zeros. The resulting impact upon filter characteristics is discussed with conclusions regarding the robustness, or otherwise, of the structures presented in chapter five. Following this, limit cycles are comprehensively discussed in the context of the options for the quantisation of signals. The problem of instability, which leads to the oscillations in question, is explored via a constructive approach leading to diagrams of coefficient regions that avoid limit cycles.

Chapter nine is a fairly short round up of the practicalities of analogue-to-digital and digital-to-analogue conversion, including the topic of oversampling that is much used in modern commercial digital signal processing devices. The appendices are gathered in a tenth chapter and cover nomenclature, sixty references, filter design tables and design programmes in Borland's Turbo Pascal.

This book fills a useful slot in the field of digital signal processing. By focussing on filters alone it remains a manageable size whilst allowing very detailed consideration of essential issues such as limit cycles. The aim is to give insight into digital filter characteristics plus design at a high level and this is achieved with a great degree of success. Although chapters one to five may be found elsewhere, the book would look very odd without them. Readers already in possession of a good digital signal processing text should still find this book worth buying for chapters six to nine alone.