A Student's Guide to Fourier Transforms, with applications in physics and engineering

This book is not suitable for the majority of readers of Physics Education. It is a highly specialized textbook which is intended to give a `concise introduction to the theory and practice of Fourier transforms ... and avoiding unnecessary mathematics'. The author states that no previous knowledge of the subject is needed. However, I believe that the subject matter will only be appreciated by readers who already have a fairly detailed knowledge of optics and electrical circuit theory, probably at third-year university level. The `new' student of physics, electrical and electronic engineering and computer science will find the book heavy going because insufficient background information is supplied; the physicist will probably benefit from reading a textbook such as Hecht's Optics. In order to support the authors' contention that Fourier methods are not a theoretical device, various important applications are employed as illustration, such as extracting information from noisy signals, designing electrical filters, treating experimental data and `cleaning' TV pictures, and so on. The first chapter introduces the Fourier transform, and is relatively easy reading, but the second chapter is too highly condensed. It touches on the Dirichlet conditions, introduces some of the theorems used to manipulate Fourier pairs and then devotes much of the remainder of the chapter to the concept of the convolution. There is a tremendous amount of detail which the unfamiliar reader may find quite daunting. It is a pity that the convolution of two top-hat functions is not generated diagramatically: the author assumes that the result (a triangle) is obvious from inspection. The remaining chapters deal with the applications mentioned previously. The book has an attractive cover, and is well produced using good quality paper. I would expect the book to be bought by libraries rather than private individuals.