×

Digital filters. Theory and applications. (English) Zbl 0588.94011

Amsterdam: North-Holland (Elsevier Science Publishers). Xxiv, 496 p. $ 44.95; Dfl. 170.00 (1985).
At present, digital filtering may be considered a useful tool in such diverse areas as time series analysis, spatial data transformations, numerical analysis.
Chapter 1 of the book briefly reviews the fundamentals of the linear time-invariant digital filters. This class of systems can be analyzed using powerful transform domain techniques like Fourier transform, z-transform, etc. Stability and tests for stability, discrete convolution and deconvolution are discussed. Chapter 2 is devoted to more complex recent results from Fourier series, (discrete) Fourier transform, Euclid’s algorithm, Chinese remainder theorem, discrete Hilbert transform, Winograd’s multiplicative complexity theory, number theoretic transforms and polynomial transforms, since the topic of algebraic computational complexity is of crucial importance in the implementation of digital filters. In Chapters 3 and 4, the various types of design methods for infinite, respectively finite, impulse response digital filters are presented. In error analysis (Chapter 5), the effects of quantization, coefficient inaccuracy due to representation by finite number of bits, multiplication round-off error, problems of adder overflow and limit cycle oscillations are discussed. The contents of Chapter 6, like Chapter 2, are concerned with the improvements in the computational complexity of the problems occurring in digital filtering. Classes of matrices (Toeplitz, Hankel, circulant), orthogonal polynomials, continued fraction expansions are used to obtain the results. Chapter 7 covers special topics in digital filtering: theory of binary digital systems, 2-dimensional linear shift (-invariant and - variant) digital filters.
It is important to mention that the book provides many suggestive figures, FORTRAN programs for the most important algorithms, and numerous instructive problems at the end of every chapter. These further increase the high quality of the book as a textbook. Conceived as an excellent course in digital filters for graduate students, supplied with a modern mathematical apparatus, the book is highly suitable for the self-study of practicing engineers and scientists.

MSC:

94C05 Analytic circuit theory
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
94-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory
94-02 Research exposition (monographs, survey articles) pertaining to information and communication theory
94-04 Software, source code, etc. for problems pertaining to information and communication theory