Krishna, Hari,
Digital Signal Processing Algorithms : Number Theory, Convolution, Fast Fourier Transforms, and Applications / Hari Krishna. - First edition. - 1 online resource : text file, PDF
Chapter 1 Introduction -- part I Computational Number Theory -- Scalar and Polynomial Algebra -- chapter Thoughts on Part I -- chapter 2 Computational Number Theory -- chapter 3 Polynomial Algebra -- chapter 4 Theoretical Aspects of the Discrete Fourier Transform and Convolution -- chapter 5 Cyclotomic Polynomial Factorization and Associated Fields -- chapter 6 Cyclotomic Polynomial Factorization In Finite Fields -- chapter 7 Finite Integer Rings: Polynomial Algebra and Cyclotomie Factorization -- part II Convolution Algorithms -- chapter Thoughts on Part II -- chapter 8 Fast Algorithms for Acyclic Convolution -- chapter 9 Fast One-Dimensional Cyclic Convolution Algorithms -- chapter 10 Two- and Higher-Dimensional Cyclic Convolution Algorithms -- chapter 11 Validity of Fast Algorithms Over Different Number Systems -- chapter 12 Fault Tolerance for Integer Sequences -- part III Fast Fourier Transform (FFT) Algorithms -- chapter Thoughts on Part III -- chapter 13 Fast Fourier Transform: One Dimensional Data Sequences -- chapter 14 Fast Fourier Transforms: Multi-Dimensional Data Sequences -- part IV Recent Results on Algorithms in Finite Integer Rings -- chapter Thoughts on Part IV -- chapter Paper one A Number Theoretic Approach to Fast Algorithms for Two-Dimensional Digital Signal Processing in Finite Integer Rings -- chapter Paper two On Fast Algorithms for One Dimensional Digital Signal Processing in Finite Integer and Complex Integer Rings -- chapter Paper three Cyclotomic Polynomial Factorization in Finite Integer Rings with Applications to Digital Signal Processing -- chapter Paper four Error Control Techniques for Data Sequences Defined in Finite Integer Rings.
"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."--Provided by publisher.
9781351454971 1351454978 9781315141312 1315141310 9781351454957 1351454951
Signal processing--Digital techniques--Mathematics.
Algorithms.
TK5102.9 / K757 2017
621.3822015118
Digital Signal Processing Algorithms : Number Theory, Convolution, Fast Fourier Transforms, and Applications / Hari Krishna. - First edition. - 1 online resource : text file, PDF
Chapter 1 Introduction -- part I Computational Number Theory -- Scalar and Polynomial Algebra -- chapter Thoughts on Part I -- chapter 2 Computational Number Theory -- chapter 3 Polynomial Algebra -- chapter 4 Theoretical Aspects of the Discrete Fourier Transform and Convolution -- chapter 5 Cyclotomic Polynomial Factorization and Associated Fields -- chapter 6 Cyclotomic Polynomial Factorization In Finite Fields -- chapter 7 Finite Integer Rings: Polynomial Algebra and Cyclotomie Factorization -- part II Convolution Algorithms -- chapter Thoughts on Part II -- chapter 8 Fast Algorithms for Acyclic Convolution -- chapter 9 Fast One-Dimensional Cyclic Convolution Algorithms -- chapter 10 Two- and Higher-Dimensional Cyclic Convolution Algorithms -- chapter 11 Validity of Fast Algorithms Over Different Number Systems -- chapter 12 Fault Tolerance for Integer Sequences -- part III Fast Fourier Transform (FFT) Algorithms -- chapter Thoughts on Part III -- chapter 13 Fast Fourier Transform: One Dimensional Data Sequences -- chapter 14 Fast Fourier Transforms: Multi-Dimensional Data Sequences -- part IV Recent Results on Algorithms in Finite Integer Rings -- chapter Thoughts on Part IV -- chapter Paper one A Number Theoretic Approach to Fast Algorithms for Two-Dimensional Digital Signal Processing in Finite Integer Rings -- chapter Paper two On Fast Algorithms for One Dimensional Digital Signal Processing in Finite Integer and Complex Integer Rings -- chapter Paper three Cyclotomic Polynomial Factorization in Finite Integer Rings with Applications to Digital Signal Processing -- chapter Paper four Error Control Techniques for Data Sequences Defined in Finite Integer Rings.
"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."--Provided by publisher.
9781351454971 1351454978 9781315141312 1315141310 9781351454957 1351454951
Signal processing--Digital techniques--Mathematics.
Algorithms.
TK5102.9 / K757 2017
621.3822015118