This self-contained guide, the only one of its kind, enables engineers to find the optimum algorithm for a specific application.

Richard E. Blahut is a Professor of Electrical and Computer Engineering at the University of Illinois, Urbana-Champaign. He is Life Fellow of the IEEE and the recipient of many awards including the IEEE Alexander Graham Bell Medal (1998) and Claude E. Shannon Award (2005), the Tau Beta Pi Daniel C. Drucker Eminent Faculty Award, and the IEEE Millennium Medal. He was named a Fellow of the IBM Corporation where he worked for over 30 years in 1980, and was elected to the National Academy of Engineering in 1990.

1. Introduction; 2. Introduction to abstract algebra; 3. Fast algorithms for the discrete Fourier transform; 4. Fast algorithms based on doubling strategies; 5. Fast algorithms for short convolutions; 6. Architecture of filters and transforms; 7. Fast algorithms for solving Toeplitz systems; 8. Fast algorithms for trellis search; 9. Numbers and fields; 10. Computation in finite fields and rings; 11. Fast algorithms and multidimensional convolutions; 12. Fast algorithms and multidimensional transforms; Appendices: A. A collection of cyclic convolution algorithms; B. A collection of Winograd small FFT algorithms.