Digital Signal Processing Algorithms: Number Theory, Convolution, Fast Fourier Transforms, and Applications

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CRC Press, Mar 25, 1998 - Technology & Engineering - 672 pages
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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.
 

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Contents

Introduction
1
FAST FOURIER TRANSFORM FFT
2
Thoughts on Part I
9
Polynomial Algebra
35
Theoretical Aspects of the Discrete Fourier Transform
67
Cyclotomic Polynomial Factorization and Associated Fields
91
Cyclotomic Polynomial Factorization in Finite Fields
125
Polynomial Algebra and Cyclotomic
151
Fault Tolerance for Integer Sequences
401
Thoughts on Part III
427
OneDimensional Data Sequences
433
Multidimensional Data Sequences
493
Thoughts on Part IV
525
A Number Theoretic Approach to Fast Algorithms
531
Properties of Polynomial Transforms Over Zp for V q q
552
On Fast Algorithms for OneDimensional Digital Signal
561

Thoughts on Part II
227
Fast Algorithms for Acyclic Convolution
233
Fast OneDimensional Cyclic Convolution Algorithms
275
Two and HigherDimensional Cyclic Convolution Algorithms
337
Validity of Fast Algorithms Over Different Number Systems
381
Cyclotomic Polynomial Factorization in Finite Integer
585
Error Control Techniques for Data Sequences Defined
605
APPENDIX A Small Length Acyclic Convolution Algorithms
619
Index
633
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