Multiplicative complexity, convolution, and the DFT:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1988
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 155 S. |
| ISBN: | 0387968105 3540968105 |
Staff View
MARC
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| 245 | 1 | 0 | |a Multiplicative complexity, convolution, and the DFT |c Michael T. Heideman. C. S. Burrus, consulting ed. |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1988 | |
| 300 | |a VIII, 155 S. | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a Zugl.: Houston, Rice Univ., Diss. u.d.T.: Heideman, Michael T.: Applications of multiplicative complexity theory to convolution and the discrete Fourier transform | ||
| 650 | 7 | |a FFT |2 inriac | |
| 650 | 7 | |a complexité calcul |2 inriac | |
| 650 | 7 | |a convolution |2 inriac | |
| 650 | 7 | |a multiplication polynomiale |2 inriac | |
| 650 | 7 | |a système bilinéaire |2 inriac | |
| 650 | 7 | |a système linéaire |2 inriac | |
| 650 | 7 | |a théorie complexité |2 inriac | |
| 650 | 7 | |a transformée Fourier |2 inriac | |
| 650 | 4 | |a Computational complexity | |
| 650 | 4 | |a Convolutions (Mathematics) | |
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Record in the Search Index
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| adam_text | Contents
Chapter 1. Introduction 1
1.1. An Overview of Multiplicative Complexity 1
1.2. Why Count Only Multiplications and Divisions? 2
1.3. Organization 3
Chapter 2. Multiplicative Complexity of Linear and Bilinear Systems 5
2.1. Historical Perspective 5
2.2. Definitions and Basic Results 6
2.3. Semilinear Systems 11
2.4. Quadratic and Bilinear Systems 14
2.4.1. Properties of Quadratic Systems 14
2.4.2. Bilinear Systems and Noncommutative Algorithms 18
2.4.3. Direct Products and Direct Sums of Systems 24
2.5. Summary of Chapter 2 25
Chapter 3. Convolution and Polynomial Multiplication 27
3.1. Aperiodic Convolution / Polynomial Multiplication 27
3.2. Polynomial Multiplication Modulo an Irreducible Polynomial 31
3.3. Polynomial Multiplication Modulo a General Polynomial 34
3.4. Products of a Fixed Polynomial with Several Polynomials 36
3.4.1. Equivalent Systems and Row Reduced Forms 37
3.4.2. Reduction and Inflation Mappings 38
3.4.3. Equivalence of Products with a Fixed Polynomial 39
3.4.4. Multiplicative Complexity Results 45
3.5. Products with Several Fixed Polynomials in the Same Ring 48
3.6. Products with Several Fixed Polynomials in Different Rings 52
3.7. Multivariate Polynomial Multiplication 52
3.7.1. Polynomial Products in Two Variables 53
3.7.2. Multidimensional Cyclic Convolution 57
3.8. Summary of Chapter 3 59
Chapter 4. Constrained Polynomial Multiplication 61
4.1. General Input Constraints 61
viii
4.2. Multiplication by a Symmetric Polynomial 66
4.3. Multiplication by an Antisymmetric Polynomial 67
4.4. Products of Two Symmetric Polynomials 68
4.5. Polynomial Multiplication with Restricted Outputs 69
4.5.1. Decimation of Outputs 69
4.5.2. Other Output Restrictions 73
4.6. Summary of Chapter 4 74
Chapter 5. Multiplicative Complexity of Discrete Fourier Transform 76
5.1. The Discrete Fourier Transform 76
5.2. Prime Lengths 77
5.2.1. Rader s Permutation 77
5.2.2. Multiplicative Complexity 78
5.3. Powers of Prime Lengths 81
5.4. Power of Two Lengths 90
5.5. Arbitrary Lengths 96
5.6. DFTs with Complex Valued Inputs 105
5.7. Multidimensional DFTs 105
5.8. Summary of Chapter 5 107
Chapter 6. Restricted and Constrained DFTs 108
6.1. Restricting DFT Outputs to One Point 108
6.2. Constraining DFT Inputs to One Point 110
6.3. DFTs with Symmetric Inputs 110
6.4. Discrete Hartley Transform 115
6.5. Discrete Cosine Transform 116
6.6. Summary of Chapter 6 117
Appendix A. Cyclotomic Polynomials and Their Properties 119
Appendix B. Complexities of Multidimensional Cyclic Convolutions 123
Appendix C. Programs for Computing Multiplicative Complexity 127
Appendix D. Tabulated Complexities of the One Dimensional DFT 137
Problems 143
Bibliography 147
Index 151
|
| any_adam_object | 1 |
| author | Heideman, Michael T. |
| author_facet | Heideman, Michael T. |
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| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Thesis Book |
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| indexdate | 2024-07-09T15:36:10Z |
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| isbn | 0387968105 3540968105 |
| language | English |
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| spelling | Heideman, Michael T. Verfasser aut Multiplicative complexity, convolution, and the DFT Michael T. Heideman. C. S. Burrus, consulting ed. New York [u.a.] Springer 1988 VIII, 155 S. txt rdacontent n rdamedia nc rdacarrier Zugl.: Houston, Rice Univ., Diss. u.d.T.: Heideman, Michael T.: Applications of multiplicative complexity theory to convolution and the discrete Fourier transform FFT inriac complexité calcul inriac convolution inriac multiplication polynomiale inriac système bilinéaire inriac système linéaire inriac théorie complexité inriac transformée Fourier inriac Computational complexity Convolutions (Mathematics) Fourier transformations Faltung Mathematik (DE-588)4141470-6 gnd rswk-swf Berechnungskomplexität (DE-588)4134751-1 gnd rswk-swf Komplexitätstheorie (DE-588)4120591-1 gnd rswk-swf Diskrete Fourier-Transformation (DE-588)4150175-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Faltung Mathematik (DE-588)4141470-6 s Berechnungskomplexität (DE-588)4134751-1 s DE-604 Diskrete Fourier-Transformation (DE-588)4150175-5 s Komplexitätstheorie (DE-588)4120591-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001210906&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Heideman, Michael T. Multiplicative complexity, convolution, and the DFT FFT inriac complexité calcul inriac convolution inriac multiplication polynomiale inriac système bilinéaire inriac système linéaire inriac théorie complexité inriac transformée Fourier inriac Computational complexity Convolutions (Mathematics) Fourier transformations Faltung Mathematik (DE-588)4141470-6 gnd Berechnungskomplexität (DE-588)4134751-1 gnd Komplexitätstheorie (DE-588)4120591-1 gnd Diskrete Fourier-Transformation (DE-588)4150175-5 gnd |
| subject_GND | (DE-588)4141470-6 (DE-588)4134751-1 (DE-588)4120591-1 (DE-588)4150175-5 (DE-588)4113937-9 |
| title | Multiplicative complexity, convolution, and the DFT |
| title_auth | Multiplicative complexity, convolution, and the DFT |
| title_exact_search | Multiplicative complexity, convolution, and the DFT |
| title_full | Multiplicative complexity, convolution, and the DFT Michael T. Heideman. C. S. Burrus, consulting ed. |
| title_fullStr | Multiplicative complexity, convolution, and the DFT Michael T. Heideman. C. S. Burrus, consulting ed. |
| title_full_unstemmed | Multiplicative complexity, convolution, and the DFT Michael T. Heideman. C. S. Burrus, consulting ed. |
| title_short | Multiplicative complexity, convolution, and the DFT |
| title_sort | multiplicative complexity convolution and the dft |
| topic | FFT inriac complexité calcul inriac convolution inriac multiplication polynomiale inriac système bilinéaire inriac système linéaire inriac théorie complexité inriac transformée Fourier inriac Computational complexity Convolutions (Mathematics) Fourier transformations Faltung Mathematik (DE-588)4141470-6 gnd Berechnungskomplexität (DE-588)4134751-1 gnd Komplexitätstheorie (DE-588)4120591-1 gnd Diskrete Fourier-Transformation (DE-588)4150175-5 gnd |
| topic_facet | FFT complexité calcul convolution multiplication polynomiale système bilinéaire système linéaire théorie complexité transformée Fourier Computational complexity Convolutions (Mathematics) Fourier transformations Faltung Mathematik Berechnungskomplexität Komplexitätstheorie Diskrete Fourier-Transformation Hochschulschrift |
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| work_keys_str_mv | AT heidemanmichaelt multiplicativecomplexityconvolutionandthedft |