Unlike previous books on wavelet analysis, this work starts with basic mathematical theory not specifically developed for wavelet analysis and then applies it to the development of filtering theory, interpolation, Fourier analysis and, finally, wavelet analysis. Most of the topics examined are accompanied by pseudocode subroutines.

The book contains ten chapters, three appendices, a bibliography of 118 items, and a good index. The first chapter deals with basic mathematics: function spaces and Lebesgue integration, orthogonal functions, and approximation.

The second chapter explains the author’s philosophy for the display of program examples. He chooses pseudocode but claims that the same examples in standard C are available as an extra; unfortunately, although it is stated in several places that the means of obtaining the relevant floppy disc is given at the end of the book, this is not the case and the information is nowhere to be found. The particular pseudocode chosen is confusing: it combines LISP; BASIC, as in “FOR x=a to b” and “Let a=b”; and C, as in “x+=a.” A particularly bad feature is that loops are neither terminated by NEXT or END IF as in BASIC or by appropriate braces as in C. The reader is left to deduce the ends of structures from the indentations. The C structure notation X.Y is unnecessary in most of the cases where it is used.

The next four chapters cover the discrete Fourier transform and the fast Fourier transform and lead to a discussion of quadrature filters, defined to be convolution and decimation operators. All of this material is interesting and well presented. The student examples that end the chapters are especially interesting.

All of this accounts for about half of the book. The second half addresses wavelets. It begins with a short account of their historical background and of real and complex discrete wavelet transforms. This material is followed by various algorithms, multidimensional wavelet trees, and an examination of time-frequency analysis in relation to acoustic and other signal analysis. Finally, the author covers six specific examples: picture compression, factor analysis, matrix multiplication, speech segmentation, scrambling, and noise removal. Of particular interest is the material on picture analysis and fingerprint classification.

The appendices provide solutions to examples, a list of symbols, and sets of quadrature filter coefficients. This is a good and comprehensive book that, with the reservations mentioned above, I would recommend as a student text.