ABSTRACT
Digital Signal Processing Algorithms describes computational number theory and its applications to deriving fast algorithms for digital signal processing. It demonstrates the importance of computational number theory in the design of digital signal processing algorithms and clearly describes the nature and structure of the algorithms themselves. The book has two primary focuses: first, it establishes the properties of discrete-time sequence indices and their corresponding fast algorithms; and second, it investigates the properties of the discrete-time sequences and the corresponding fast algorithms for processing these sequences.
Digital Signal Processing Algorithms examines three of the most common computational tasks that occur in digital signal processing; namely, cyclic convolution, acyclic convolution, and discrete Fourier transformation. The application of number theory to deriving fast and efficient algorithms for these three and related computationally intensive tasks is clearly discussed and illustrated with examples.
Its comprehensive coverage of digital signal processing, computer arithmetic, and coding theory makes Digital Signal Processing Algorithms an excellent reference for practicing engineers. The authors' intent to demystify the abstract nature of number theory and the related algebra is evident throughout the text, providing clear and precise coverage of the quickly evolving field of digital signal processing.
TABLE OF CONTENTS
chapter 1|8 pages
Introduction
part I|2 pages
Computational Number Theory
chapter |2 pages
Thoughts on Part I
chapter 2|24 pages
Computational Number Theory
chapter 3|32 pages
Polynomial Algebra
chapter 4|24 pages
Theoretical Aspects of the Discrete Fourier Transform and Convolution
chapter 5|33 pages
Cyclotomic Polynomial Factorization and Associated Fields
chapter 6|26 pages
Cyclotomic Polynomial Factorization In Finite Fields
chapter 7|74 pages
Finite Integer Rings: Polynomial Algebra and Cyclotomie Factorization
part II|2 pages
Convolution Algorithms
chapter |6 pages
Thoughts on Part II
chapter 8|42 pages
Fast Algorithms for Acyclic Convolution
chapter 9|62 pages
Fast One-Dimensional Cyclic Convolution Algorithms
chapter 10|44 pages
Two- and Higher-Dimensional Cyclic Convolution Algorithms
chapter 11|20 pages
Validity of Fast Algorithms Over Different Number Systems
chapter 12|2 pages
Fault Tolerance for Integer Sequences
part III|2 pages
Fast Fourier Transform (FFT) Algorithms
chapter |6 pages
Thoughts on Part III
chapter 13|60 pages
Fast Fourier Transform: One Dimensional Data Sequences
chapter 14|30 pages
Fast Fourier Transforms: Multi-Dimensional Data Sequences
part IV|2 pages
Recent Results on Algorithms in Finite Integer Rings