Fast Fourier Transform and Convolution Algorithms:
Gespeichert in:
1. Verfasser: | |
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1981
|
Schriftenreihe: | Springer Series in Information Sciences
2 |
Schlagworte: | |
Online-Zugang: | Volltext |
Beschreibung: | This book presents in a unified way the various fast algorithms that are used for the implementation of digital filters and the evaluation of discrete Fourier transforms. The book consists of eight chapters. The first two chapters are devoted to background information and to introductory material on number theory and polynomial algebra. This section is limited to the basic concepts as they apply to other parts of the book. Thus, we have restricted our discussion of number theory to congruences, primitive roots, quadratic residues, and to the properties of Mersenne and Fermat numbers. The section on polynomial algebra deals primarily with the divisibility and congruence properties of polynomials and with algebraic computational complexity. The rest of the book is focused directly on fast digital filtering and discrete Fourier transform algorithms. We have attempted to present these techniques in a unified way by using polynomial algebra as extensively as possible. This objective has led us to reformulate many of the algorithms which are discussed in the book. It has been our experience that such a presentation serves to clarify the relationship between the algorithms and often provides clues to improved computation techniques. Chapter 3 reviews the fast digital filtering algorithms, with emphasis on algebraic methods and on the evaluation of one-dimensional circular convolutions. Chapters 4 and 5 present the fast Fourier transform and the Winograd Fourier transform algorithm |
Beschreibung: | 1 Online-Ressource |
ISBN: | 9783662005514 9783662005538 |
ISSN: | 0720-678X |
DOI: | 10.1007/978-3-662-00551-4 |
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discipline | Physik Mathematik |
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spelling | Nussbaumer, Henri J. Verfasser aut Fast Fourier Transform and Convolution Algorithms by Henri J. Nussbaumer Berlin, Heidelberg Springer Berlin Heidelberg 1981 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Springer Series in Information Sciences 2 0720-678X This book presents in a unified way the various fast algorithms that are used for the implementation of digital filters and the evaluation of discrete Fourier transforms. The book consists of eight chapters. The first two chapters are devoted to background information and to introductory material on number theory and polynomial algebra. This section is limited to the basic concepts as they apply to other parts of the book. Thus, we have restricted our discussion of number theory to congruences, primitive roots, quadratic residues, and to the properties of Mersenne and Fermat numbers. The section on polynomial algebra deals primarily with the divisibility and congruence properties of polynomials and with algebraic computational complexity. The rest of the book is focused directly on fast digital filtering and discrete Fourier transform algorithms. We have attempted to present these techniques in a unified way by using polynomial algebra as extensively as possible. This objective has led us to reformulate many of the algorithms which are discussed in the book. It has been our experience that such a presentation serves to clarify the relationship between the algorithms and often provides clues to improved computation techniques. Chapter 3 reviews the fast digital filtering algorithms, with emphasis on algebraic methods and on the evaluation of one-dimensional circular convolutions. Chapters 4 and 5 present the fast Fourier transform and the Winograd Fourier transform algorithm Mathematics Numerical analysis Numerical Analysis Mathematik Faltung Mathematik (DE-588)4141470-6 gnd rswk-swf Fourier-Transformation (DE-588)4018014-1 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Schnelle Fourier-Transformation (DE-588)4136070-9 gnd rswk-swf Schneller Faltungsalgorithmus (DE-588)4179867-3 gnd rswk-swf Digitalfilter (DE-588)4070477-4 gnd rswk-swf Schnelle Fourier-Transformation (DE-588)4136070-9 s Algorithmus (DE-588)4001183-5 s 1\p DE-604 Digitalfilter (DE-588)4070477-4 s Faltung Mathematik (DE-588)4141470-6 s 2\p DE-604 3\p DE-604 4\p DE-604 Schneller Faltungsalgorithmus (DE-588)4179867-3 s 5\p DE-604 Fourier-Transformation (DE-588)4018014-1 s 6\p DE-604 https://doi.org/10.1007/978-3-662-00551-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Nussbaumer, Henri J. Fast Fourier Transform and Convolution Algorithms Mathematics Numerical analysis Numerical Analysis Mathematik Faltung Mathematik (DE-588)4141470-6 gnd Fourier-Transformation (DE-588)4018014-1 gnd Algorithmus (DE-588)4001183-5 gnd Schnelle Fourier-Transformation (DE-588)4136070-9 gnd Schneller Faltungsalgorithmus (DE-588)4179867-3 gnd Digitalfilter (DE-588)4070477-4 gnd |
subject_GND | (DE-588)4141470-6 (DE-588)4018014-1 (DE-588)4001183-5 (DE-588)4136070-9 (DE-588)4179867-3 (DE-588)4070477-4 |
title | Fast Fourier Transform and Convolution Algorithms |
title_auth | Fast Fourier Transform and Convolution Algorithms |
title_exact_search | Fast Fourier Transform and Convolution Algorithms |
title_full | Fast Fourier Transform and Convolution Algorithms by Henri J. Nussbaumer |
title_fullStr | Fast Fourier Transform and Convolution Algorithms by Henri J. Nussbaumer |
title_full_unstemmed | Fast Fourier Transform and Convolution Algorithms by Henri J. Nussbaumer |
title_short | Fast Fourier Transform and Convolution Algorithms |
title_sort | fast fourier transform and convolution algorithms |
topic | Mathematics Numerical analysis Numerical Analysis Mathematik Faltung Mathematik (DE-588)4141470-6 gnd Fourier-Transformation (DE-588)4018014-1 gnd Algorithmus (DE-588)4001183-5 gnd Schnelle Fourier-Transformation (DE-588)4136070-9 gnd Schneller Faltungsalgorithmus (DE-588)4179867-3 gnd Digitalfilter (DE-588)4070477-4 gnd |
topic_facet | Mathematics Numerical analysis Numerical Analysis Mathematik Faltung Mathematik Fourier-Transformation Algorithmus Schnelle Fourier-Transformation Schneller Faltungsalgorithmus Digitalfilter |
url | https://doi.org/10.1007/978-3-662-00551-4 |
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