Inside the FFT Black Box: Serial and Parallel Fast Fourier Transform Algorithms

Rating:
Summary: Varied, specific, and practical.
Review: If you need this book, you already know it. You barely remember what the Fourier transform does, let alone how it works, and you need to implement it from scratch. This book is for you.

Most programmers never need to use Fourier transforms. Most of the ones who do will get by quite nicely on black boxes from Mathematica, Matlab, or Numerical Recipes. Data goes in, answers come out, and "a miracle occurs" somewhere in between. There are those times, however, when you can't use the canned routines. You just have to write your own.

This book isn't for the faint-hearted, but really does give everything a non-specialist needs for creating a competent implementation. There's no cut&paste code here, but this is for people with unique needs. It presents a number of basic variations, with clear illustrations and pseudocode. It even discusses 2D transforms, but most of that discussion centers on how to transpose the 2D matrix between 1D transforms.

The discussion of parallel implementation was the only section I found weak. It's aimed at standard sorts of multiprocessors, with specific kinds of connection networks between processors. First, those networks are rare in commercial multiprocessors or are so deeply embedded that the topology is not accessible to the application writer. Second, those networks and architectures miss a lot of important computing environments completely - including the ones important to me.

I don't wish it on anyone, but it might happen - you might have to implement a FFT for yourself. If it does happen, this book may be your most effective tool. It will probably take the non-specialist (like me) time to get past some of the notation, but the answers here are worth the effort.

//wiredweird