This is an engineering cookbook that covers the more elementary aspects of computing discrete Fourier transforms (DFTs). It attempts to integrate the continuous Fourier transform into the discussion but this is not very successful.

The book has a good bit of material on the pitfalls of sampling and calculation, and many numerical examples and lots of graphs. It includes two chapters on material I had not seen before: DFTs with a large prime number of samples.

The big weakness of the book is that it has no applications. For example, there is a lot of material on windowing and on finite-impulse response (FIR) filters but no mention of why these are useful.

A good book on this subject for mathematicians, that does a better job of combining the discrete and continuous (but is much more advanced) is Claude Gasquet & Patrick Witomski's *Fourier Analysis and Applications* (Springer, 1999). Good books for engineers are Oppenheim & Willsky & Hamid's *Signals and Systems* (Prentice-Hall, 2nd editiion 1996), and the more advanced book by Oppenheim & Schafer & Buck, *Discrete-Time Signal Processing* (Prentice-Hall, 2nd edition 1999); however, these are not cookbooks.

Allen Stenger is a math hobbyist, library propagandist, and retired computer programmer. He volunteers in his spare time at MathNerds.com, a math help site that fosters inquiry learning. His mathematical interests are number theory and classical analysis.