This graduate-level text provides a language for understanding, unifying, and implementing a wide variety of algorithms for digital signal processing - in particular, to provide rules and procedures that can simplify or even automate the task of writing code for the newest parallel and vector machines. It thus bridges the gap between digital signal processing algorithms and their implementation on a variety of computing platforms. The mathematical concept of tensor product is a recurring theme throughout the book, since these formulations highlight the data flow, which is especially important on supercomputers. Because of their importance in many applications, much of the discussion centres on algorithms related to the finite Fourier transform and to multiplicative FFT algorithms.
A textbook based on courses taught at CUNY and Fudan U., Shanghai over some five years. It offers a bridge between programming and design disciplines through use of linguistic and mathematical tools. Intended for design and implementation of discrete signal processing algorithms on vector and parallel computers. Annotation c. Book News, Inc., Portland, OR (booknews.com)
1 Review of Applied Algebra.- 2 Tensor Product and Stride Permutation.- 3 Cooley-Tukey FFT Algorithms.- 4 Variants of FT Algorithms and Implementations.- 5 Good-Thomas PFA.- 6 Linear and Cyclic Convolutions.- 7 Agarwal-Cooley Convolution Algorithm.- 8 Multiplicative Fourier Transform Algorithm.- 9 MFTA: The Prime Case.- 10 MFTA: Product of Two Distinct Primes.- 11 MFTA: Composite Size.- 12 MFTA: p2.- 13 Periodization and Decimation.- 14 Multiplicative Characters and the FT.- 15 Rationality.