In recent years, old work in the field of signal engineering is being studied with fresh interest by computer scientists and mathematicians. (See the recent survey by Jorgensen [1] for an example.) The traditional engineering tools of Fourier analysis, matrix algebra, and the like are now being augmented in several cases with newer tools from algebra, functional analysis, and topology. The result is the availability of new algorithms and insights for engineers, graphic designers, computer scientists, mathematicians, and others.

The traditional Fourier transform is not particularly well suited to model discrete data, and has been supplanted by other methods. The Haar wavelet and the mother wavelet are examples. One such tool that is used in the analysis and synthesis of discrete data is the decision diagram (DD), a data structure that efficiently captures large discrete functions. (Discrete data are almost always considered equivalent to the functions that represent them, and these functions are considered equivalent to the data structures used to model them.)

Spectral interpretation of decision diagrams deals with the spectral interpretation of DDs, that is to say, the application of spectral techniques such as Reed-Muller transforms from classical signal theory to decision diagrams. The authors start by reviewing the basic notions of signal processing and the algebraic notions involved in its analysis. They then move on to a brief presentation of classical spectral techniques and Fourier analysis, before moving on to the main topics of discussion.

Inasmuch as classical computer science curricula (even at the graduate level) do not cover all the topics needed to understand this material, the book will be a hard read for many in the CS community who may be interested in its information. In spite of the authors’ efforts to present the basics before moving on to the main material, it is likely that readers and students exposed to the basics for the first time will need significant supplementary study to comprehend the material in depth.

However, electrical engineering researchers and students who do have a significant depth of understanding covering Haar transforms, Reed-Muller transforms, Fourier analysis, abstract algebra, and such other topics outside the classical CS core will definitely find the text a welcome addition to their repertoire.