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Signal processing and data analysis. (English) Zbl 1427.94001

De Gruyter STEM. Berlin: De Gruyter; Beijing: Tsinghua University Press (ISBN 978-3-11-046158-9/pbk; 978-3-11-046508-2/ebook). xvi, 586 p. (2018).
This well-written, comprehensive textbook presents the basic mathematical methods in digital signal processing. It is mainly written for graduate students in engineering disciplines and consists of 14 chapters.
Chapter 1 introduces the basic concepts of signals and systems. Fourier series and Fourier transforms are handled in Chapter 2. In Chapter 3, signals and systems are analyzed by Laplace transform and \(z\)-transform. Chapter 4 describes the discretization of continuous-time signals and the reconstruction of discrete-time signals. Properties of discrete Fourier transforms and fast algorithms of discrete Fourier transforms are presented in Chapter 5. The principles of digital filters and digital filter design are given in Chapter 6. Chapter 7 studies the finite word-length effects in digital signal processing. Several methods of error analysis and signal preprocessing are described in Chapter 8. Chapter 9 deals with basic concepts of random signal processing. Chapter 10 discusses the estimation of the correlation function and the power spectral density function of random signals. Chapter 11 studies Wiener filters and Kalman filters, and gives applications of statistical optimal filters. The adaptive filtering theory is presented in Chapter 12. Chapter 13 describes the signal processing with higher-order statistics or fractional order statistics. Finally, Chapter 14 handles selected topics in modern signal processing, such as time-frequency analysis, Gabor transforms, wavelet transforms, and Hilbert transforms.
The theory is illustrated by numerous examples, practical applications, many figures and tables. Several algorithms in MATLAB are given too. Each chapter closes with numerous exercises (without solutions). Often the exact mathematical assumptions in fundamental definitions and results are omitted. Proofs of essential results of Fourier analysis are not given. Altogether, this is a useful textbook for graduate students in engineering disciplines and a convenient reference for researchers working on digital signal processing.

MSC:

94-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
65T50 Numerical methods for discrete and fast Fourier transforms
65R10 Numerical methods for integral transforms

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