Includes bibliographical references and index.

Machine generated contents note: 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.

"Efficient signal processing algorithms are important for embedded and power-limited applications since, by reducing the number of computations, power consumption can be reduced significantly. Similarly, efficient algorithms are also critical to very large scale applications such as video processing and four-dimensional medical imaging. This self-contained guide, the only one of its kind, enables engineers to find the optimum fast algorithm for a specific application. It presents a broad range of computationally-efficient algorithms, describes their structure and implementation, and compares their relative strengths for given problems. All the necessary background mathematics is included and theorems are rigorously proved, so all the information needed to learn and apply the techniques is provided in one convenient guide. With this practical reference, researchers and practitioners in electrical engineering, applied mathematics, and computer science can reduce power dissipation for low-end applications of signal processing, and extend the reach of high-end applications"-- Provided by publisher.