Digital filtering and signal processing

Book Reviews DIGITAL FILTERING AND SIGNAL PROCESSING, by D. Childers and A. Durling. 539 pages, diagrams, 6 x 9 in. St. Paul, Minnesota, 1975. Price, $18.95. (approx. f9.85). Features common to this and other books in the same area are a not-quitecomplete analog-filter background, a lack of numerical transforms and an addiction to complexity. This book, however, contains the wrong from of numerical transforms and the overly general form of state-variable representation. Many topics, many references, much flak, and a personal writing style will hardly give any student of digital filters even a hint that digital filters can be strange as well as simple and complicated. Analog filters are better understood by concentrating on Butterworth low-pass filters. One can then perceive that a prefix and a suffix are missing from conventional analog-filter theory. The missing prefix is a definition that associates two finite amplitude bands with two frequency bands in the power spectrum of a low-pass filter. The missing suffix is filter cut-off frequency renormalization; already present are normalized and denormalized filters. There is an art and practicality to these three “normalizations” and their main result is superb house-keeping. The proper definition of low pass digital filters enables one to discard most impulseresponse techniques. The three “normalizations” are a definite need even in this book. The all-pass to all-pass transformation, 2 + (1 + ~)/(a + z), for frequency transformations that achieve high-pass, band-pass and band-rejection filters is not wrong; merely superfluous. Excess baggage is a bane for any theory! Pulse transfer functions that are not filters can be dealt with directly: or one can fall back upon numerical transforms, the corrected form of number series. Number series were thoroughly investigated in 1962 and shown to require additive terms for achieving greater accuracy.

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Moreover, the Simpson Rule for quadrature cannot be described by a fast sampler. The proper description requires a decomposition of the fast sampler that makes the Simpson Rule analogous to the tough skip-sampler. This book to this day persists in repeating two questionable assertions: (i) That fast sampling of an analog convolution results in discrete convolution; (ii) That fast sampling describes the Simpson Rule. Besides the prefix and suffix, one also requires careful proofs, testing and culling of results, and detection of voids. For instance, the Tustin bilinear substitution is intertwined with a missing state-variable representation under zero initial conditions; but this book produces a decoy counter-addition, the use of Runge-Kutta approximations to a matrix-vector differential equation motivated by linear algebra. The digital filter is not a simplifiable subject; this reviewer cautions any reader to obtain an extensive analog-filter and numerical-transform background before dabbling in digital filters. It’s greatest difficulty is strangeness. The reader can be assured, though, that the subject is finite and tractable. C. A. HALIJAK Department of Electrical Engineering University of Alabama, Huntsville, Alabama ORTHOGONAL TRANSFORMS FOR DIGITAL SIGNAL PROCESSING by N. Ahmed and K. R. Rao. 263 pages, diagrams, 6X 9 in., Springer, New York/Berlin, 1975. Price, $24.50. (approx. f12.25). As its title implies, this book describes a number of orthogonal transforms, together with their applications. The first three chapters present the standard theory of the Fourier representation of functions and vectors, and Chap. 4 describes some common forms of the fast Fourier transform. Chapters 5 and 6 are about Walsh functions and the fast Walsh transform,

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