Digital processing of signals

THERE ARE quite a few books published on the subject of digital signal processing, each contributing something different to this presently very active field. The same applies to the above-titled book by M. Bellanger, particularly so because it originates in France, and hence has a distinctly different flavour to the majority of books from other places. This book covers not only normal topics on digital filters, but also more advanced ones. It consists of 13 chapters dealing with the material as discussed below. The first chapter points out straight away that we are treating a numerical form of a signal obtained by a double approximation in time and amplitude space. It goes then into Fourier analysis and various related operations, followed by discussion of the main properties of deterministic and ramdom signals. The second half of this chapter is devoted to sampling operation, quantization, study of dynamic range and nonlinear and optimal coding. The following two chapters deal with the discrete Fourier transform (DFT). After defining the DFT algorithm, and a brief discussion of its properties, the fast Fourier transform (FFT) is introduced. The FFT technique is then gradually developed and illustrated at various stages. The degradation of FFT due to the finite wordlength is then quite thoroughly discussed which is a very good feature of this book, repeated later in other chapters. The author then returns to the DFT and discusses its filtering property, and its calculation by means of convolution (the chirp z-transform algorithm). At the end of this chapter, a brief discussion is given on the FFT implementation. The third chapter is about a unified representation of the FFT and other fast algorithms, and appears to be rather advanced. The cdmputaIional methods are developed by means of factorization of matrices and applied to the FFT. Other fast algorithms for calculation of DFT are described too. The chapter ends with the number theoretic transforms. The computational complexity of different approaches are compared in appropriate places, which is again a very good feature of this book. Chapters 4-8 cover the material on digital filtering. This starts, in Chapter 4, with an introduction to the convolution summation, followed by the z-transform definition and a brief exposition of its important properties. The power of discrete signals is then discussed and shown to be equal to the power of the frequency spectrum. The filtering of random signals is also considered which is very useful in later chapters. Towards the end of this chapter, it is shown that the transfer function of a discrete time filter is a rational polynomial in the variable z. The state variable analysis is also briefly discussed. The finite impulse response (FIR) or nonrecursive filters, are presented in Chapter 5. This starts by considering simple twoand three-coefficient filters, and shows how the frequency response is obtained by the direct application of Fourier transforms. This is further extended to N-coefficient filters and the conditions for the linear phase response are discussed. This is followed by an introduction to the standard FIR filter design based on the Fourier series expansion of a specified frequency response. It is shown that by limiting the number of coefficients.