The theory of the sampling and reconstruction of bandwidth-limited signals is the only subject of this book. Chapter 1 is a historical introduction. Chapter 2 covers “Fundamentals of Fourier Analysis and Stochastic Processes.” Chapter 3, “The Cardinal Series,” discusses developments in series expansions of (sin nt )&slash; t. Chapter 4, “Generalizations of the Sampling Theorem,” contains a reasonably up-to-date discussion of one-dimensional reconstruction processes. Chapter 5, “Sources of Error,” gives mathematically and pedagogically sound error estimates in most common situations. Chapter 6, “The Sampling Theorem in Higher Dimensions,” extends chapters 3 through 5 to n dimensions. Finally, chapter 7, on “Continuous Sampling,” covers prolate spheroidal wave functions, the Papoulis-Gerchberg algorithm, and as much of Youla’s general reconstruction algorithm as can be explained with the minimal mathematical background the author assumes.

The mathematical background given in chapter 2 is rather elementary. It also seems to assume that every integral from - ∞ to+ ∞ is a Cauchy principal value. While it is true that distribution theory deals only with principal values, and Fourier theory almost always uses them, a student who has had a decent course in distributions (or locally convex Banach spaces) will not need chapter 2; a student without this background will be sorely confused. Teachers should produce their own background material to replace this chapter, and readers who are already familiar with the material should only skim it for the notation.

The definition of uniform continuity in chapter 3 (p. 40) is impossible. The discussion of why a telephone conversation cannot be entirely reconstructed from a few words (p. 257) is erroneous (the correct explanation is that a phone conversation with globally bounded bandwidth signals would be very peculiar). Also, Figures 4.12 and 4.17 are identical, and the graphs in 4.12 do not match those produced on my monitor.

Marks states that the book is intended as a text for a second-year graduate course. The chapter problems (with selected answers in the back) and references are adequate for this purpose. The book will also give any engineer who has the mathematical background required for work in signal theory the understanding to judiciously use the algorithms discussed, with a healthy respect for error estimates.

The book is enjoyable and I recommend it. Since it was produced by desktop publishing, it is almost free of typos, and the absence of small typefaces is only a mild irritant.