The DFT: An Owners' Manual for the Discrete Fourier Transform

This book is recommended in the 2nd Edition of Fast Fourier Transforms by Walker at Wisconsin. The reason it is recommended is that Chapter 6 of The DFT by Briggs and Henson contains a very readable introduction to the subject of error in the FFT approximation. This is a topic that is often ignored because in a wide collection of circumstances the error in the FFT approximation is quite small. However, Briggs and Henson freely admit that they have only offered an introduction to the subject, and they provide deeper references.

This useful book provides a working knowledge of the DFT, with some insight of the main FFT algorithms (postponed to the Appendix). It bridges the gap between math books on the same subject, and black-box treatments of the DFT (like many books dealing with filters). Here I have found illuminating explanations about zero-padding, interpolation, windowing et Chebyshev transform. The mathematical level remains elementary throughout. Some warnings : there are neither computer programs, nor flow charts provided. Besides, whereas Gibbs' phenomenon is described and explained, the handling of it is left to further reading. However, the authors are to be commended for giving starting insights into a variety of subjects : signal and image processing, polynomial transforms, fast Poisson solvers, wavelets. To sum up: a very inspiring handbook.

Exellent! Cannot say it better! Easy to read, well laid out...all in all excellent. If you are looking for a practical DFT, look no further.