Algorithms for Discrete Fourier Transform and Convolution

This book provides a broad view of the latest developments in the field of fast Digital Signal Processing (DSP) algorithms. The purpose of this book is to offer a textbook for graduate courses and a reference book of DSP algorithms for those who are in the field of signal processing. It bridges the gap between DSP algorithms and their implementation on a variety of serial and super comput- ers. The mathematical concept of tensor product can be matched to machine implementation, and the tensor product formulation of DSP algorithms provides computer implementation options. Modifications of Winograd FFT algorithms are presented with a diversity of arithmetic (multiplications and additions) choices. The methods of tensor product formulation of DSP algorithms and multiplicative algorithms for different transform sizes are all new. The method of presenting an algorithm by its algebra structure which matches the computer architecture is a highlight of this text and makes the computer architecture easily accessible to both students and researchers.