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krishna hari - digital signal processing algorithms

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




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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

CRC Press

Pubblicazione: 03/1998
Edizione: 1° edizione





Trama

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.




Sommario

IntroductionOutlineThe OrganizationPART I: Computational Number TheoryComputational Number TheoryGroups, Rings, and FieldsElements of Number TheoryInteger Rings and FieldsChinese Remainder Theorem for IntegersNumber Theory for Finite Integer RingsPolynomial AlgebraAlgebra of Polynomials over a FieldRoots of a PolynomialPolynomial Fields and RingsThe Chinese Remainder Theorem for PolynomialsCRT-P in Matrix FormLagrange InterpolationPolynomial Algebra over GF(p)Order of an ElementTheoretical Aspects of Discrete Fourier Transform and ConvolutionThe Discrete Fourier TransformBasic Formulation of ConvolutionBounds on the Multiplicative ComplexityBasic Formulation of Convolution AlgorithmsMatrix Exchange PropertyCyclotomic Polynomial Factorization and Associated FieldsCyclotomic Polynomial Factorization over Complex and Real NumbersCyclotomic Polynomial Factorization over Rational NumbersCyclotomic Fields and Cyclotomic Polynomial FactorizationsExtension Fields of Cyclotomic Fields and Cyclotomic Polynomial FactorizationA Preview of Applications to Digital Signal ProcessingCyclotomic Polynomial Factorization in Finite FieldsCyclotomic Polynomial FactorizationFactorization of (un - 1) over GF (p)Primitive Polynomials over GF (p)Complex Finite Fields and Cyclotomic Polynomial FactorizationFinite Integer Rings: Polynomial Algebra and Cyclotomic FactorizationPolynomial Algebra over a RingLagrange InterpolationNumber Theoretic TransformsMonic Polynomial FactorizationExtension of CRT-P over Finite Integer RingsPolynomial Algebra and CRT-PR: The Complex CaseNumber Theoretic Transforms: The Complex CasePseudo Number Theoretic TransformsPolynomial Algebra and Direct Sum Properties in Integer Polynomial RingsPART II: Convolution AlgorithmsThoughts on Part IIFast Algorithms for Acyclic ConvolutionCRT-P Based Fast Algorithms for One-Dimensional Acyclic ConvolutionCasting the Algorithm in Bilinear FormulationMultidimensional Approaches to One-Dimensional Acyclic ConvolutionMultidimensional Acyclic Convolution AlgorithmsNesting and Split Nesting Algorithms for Multidimensional ConvolutionAcyclic Convolution Algorithms over Finite Fields and RingsFast One-Dimensional Cyclic Convolution AlgorithmsBilinear Forms and Cyclic ConvolutionCyclotomic Polynomials and Related Algorithms over Re and CCyclotomic Polynomials and Related Algorithms over ZOther ConsiderationsComplex Cyclotomic Polynomials and Related Algorithms over CZThe Agarwal-Cooley AlgorithmCyclic Convolution Algorithms over Finite Fields and RingsTwo- and Higher Dimensional Cyclic Convolution AlgorithmsPolynomial Formulation and an AlgorithmImprovements and Related AlgorithmsDiscrete Fourier Transform Based AlgorithmsAlgorithms Based on Extension FieldsAlgorithms for Multidimensional Cyclic ConvolutionAlgorithms for Two-Dimensional Cyclic Convolution in Finite Integer RingsValidity of Fast Algorithms over Different Number SystemsIntroductionMathematical PreliminariesChinese Remainder Theorem over Finite Integer RingsInterrelationships among Algorithms over Different Number SystemsAnalysis of Two-Dimensional Cyclic Convolution AlgorithmsFault Tolerance for Integer SequencesA Framework for Fault ToleranceMathematical Structure of C over Z(M)Coding Techniques over Z(q)Examples and SFC-DFD CodesPART III: Fast Fourier Transform (FFT) AlgorithmsThoughts on Part IIIFast Fourier Transform: One-Dimensional Data SequencesThe DFT: Definitions and PropertiesRader's FFT Algorithm, n=p, p an Odd PrimeRader's FFT Algorithm, n=pc, p an Odd PrimeCooley-Tukey FFT Algorithm, n=a . bFFT Algorithms for n a Power of 2The Prime Factor FFT n=a . b, (a,b) =1The Winograd FFT AlgorithmFast Fourier Transform: Multidimensional Data SequencesThe Multidimensional DFT: Definition and PropertiesFFT for n=p, p an Odd PrimeMultidimensional FFT Algorithms for n a Power of 2Matrix Formulation of Multidimensional DFT and Related AlgorithmsPolynomial Version of Rader's AlgorithmPolynomial Transform Based FFT AlgorithmsPART IV: Recent Results on Algorithms in Finite Integer RingsThoughts on Part IVPaper One: A Number Theoretic Approach to Fast Algorithms for Two-Dimensional Digital Signal Processing in Finite Integer RingsPaper Two: On Fast Algorithms for One-Dimensional Digital Signal Processing in Finite Integer and Complex Integer RingsPaper Three: Cyclotomic Polynomial Factorization in Finite Integer Rings with Applications to Digital Signal ProcessingPaper Four: Error Control Techniques for Data Sequences Defined in Finite Integer RingsA. Small Length Acyclic Convolution AlgorithmsB. Classification of Cyclotomic PolynomialsIndex










Altre Informazioni

ISBN:

9780849371783

Condizione: Nuovo
Collana: Computer Science & Engineering
Dimensioni: 9.25 x 6.25 in Ø 2.35 lb
Formato: Copertina rigida
Illustration Notes:23 tables
Pagine Arabe: 672


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