Book Review: Discrete Transforms

Discrete Transforms: J. M. FIRTH (Chapman & Hall, 1992, 187pp., £12.95) The analysis ofsignalsand systemsis a wideand important topic in engineeringand so are the tools for this analysis.This book deals with transform methods and includesFourier transform, convolution,z-transform,discrete Fourier transform,fast Fourier transform and Hartley transform.An exhaustivelist of books whichcovers this subject are easilyavailable and especially books on digital signal processing.This entire book howeverdeals only with the specific above mentioned transformsand thereforethe reader can look in some detail at each transform, compare them and therefore the use of each specific application becomesobvious. The material in this book is covered in 6 chapters. Chapters I and 2 introduce the Fourier series, Fourier transform, Laplace transform and convolution. The relationship betweenthe onesided Laplace transform and Fourier transforms is also referredto. Chapter 3 introduces the notion of sampling and its effects on the spectrum, such as periodicityand aliassing. The chapter also includeswindowingand explains the transition from the Laplace transform to the z-transform. Chapter 4 is mainlyconcerned with the application of the z-transform for the solution of difference equation and shows how linear difference equations with a constant parameter is derived from the approximation of a differential equation. Chapter 5 shows that by applying numericalintegration and series truncation to the Fourier seriespair, the discrete Fourier transform and its inversecan be obtained. The properties of the transform pair have also been developed. The last chapter deals with fast Fourier transform algorithms and this involvesthe discrete Fourier transform matrix and signal flow. This is a useful book for anyone dealing with the transform mentionedabove or with digital signalprocessing. Usefulworked examplesare giventhroughout the text. N. DAHNOUN Department of Electrical Engineering and Electronics, UMIST