Mathematics of multidimensional Fourier transform algorithms:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1993
|
| Series: | Signal processing and digital filtering
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XIV, 233 S. |
| ISBN: | 3540941053 0387941053 |
Staff View
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| 245 | 1 | 0 | |a Mathematics of multidimensional Fourier transform algorithms |c Richard Tolimieri ; Myoung An ; Chao Lu |
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Record in the Search Index
| _version_ | 1823026246795132928 |
|---|---|
| adam_text |
RICHARD TOLIMIERI MYOUNG AN CHAO LU
MATHEMATICS OF
MULTIDIMENSIONAL
FOURIER
TRANSFORM
ALGORITHMS
CS.
BURRUS
CONSULTING
EDITOR
SPRINGER-VERLAG
NEW YORK BERLIN HEIDELBERG LONDON PARIS
TOKYO
HONG KONG BARCELONA BUDAPEST
*.
CONTENTS
PREFACE V
LIST OF SYMBOLS AND NOTATION XIII
1 TENSOR PRODUCT 1
1.1 INTRODUCTION 1
1.2 TENSOR PRODUCT 2
1.3 STRIDE PERMUTATIONS 7
1.4 ALGEBRA OF STRIDE PERMUTATIONS 10
1.5 TENSOR PRODUCT FACTORIZATION 11
1.6 FAST FOURIER TRANSFORM ALGORITHMS I 16
1.7 GENERAL 1-DIMENSIONAL FFT 20
BIBLIOGRAPHY 24
PROBLEMS 28
2 MULTIDIMENSIONAL TENSOR PRODUCT AND FFT 29
2.1 INTRODUCTION 29
2.2 MULTIDIMENSIONAL FOURIER TRANSFORM 31
2.3 2-DIMENSIONAL OPERATIONS 33
2.4 2-DIMENSIONAL COOLEY-TUKEY FFT 38
BIBLIOGRAPHY 41
PROBLEMS 42
3 FINITE ABELIAN GROUPS 45
3.1 INTRODUCTION 45
3.2 CHARACTER GROUP 46
3.3 DUALITY 53
^
YY
X
CONTENTS
3.4 CHINESE REMAINDER THEOREM 55
3.5 VECTOR SPACE
L(A)
59
BIBLIOGRAPHY 61
PROBLEMS . . 61
4 FOURIER TRANSFORM OF FINITE ABELIAN GROUPS 63
4.1 INTRODUCTION 63
4.2 FOURIER TRANSFORM OF
A
64
4.3 INDUCED FOURIER TRANSFORM 66
4.4 PERIODIC AND DECIMATED DATA 67
4.5 PERIODIZATION AND DECIMATION 71
BIBLIOGRAPHY 75
5 COOLEY-TUKEY AND GOOD-THOMAS 77
5.1 INTRODUCTION 77
5.2 GOOD-THOMAS FFT 78
5.3 ABSTRACT COOLEY-TUKEY FFT 80
BIBLIOGRAPHY 86
6 LINES 89
6.1 INTRODUCTION 81
6.2 EXAMPLES 90
6.3 PRIMECASE 94
6.4 PRIME POWER CASE 96
6.5 SQUARE CASE 102
6.6 RECTANGULAR CASE 108
BIBLIOGRAPHY 112
PROBLEMS 113
7 DUALITY OF LINES AND PLANES 115
7.1 AUTOMORPHISM GROUP 115
7.2 DUAL OF LINES 121
7.3 PLANES AND DUALITY 125
BIBLIOGRAPHY 131
PROBLEMS 132
CONTENTS
XI
8 REDUCED TRANSFORM ALGORITHMS 135
8.1 INTRODUCTION 135
8.2 GENERAL STRUCTURE 136
8.3 PERIODIZATIONS 138
8.4 EXAMPLES 141
8.4.1 CASE
M = P, P
A PRIME 141
8.4.2 CASE
M =
P
2
,
P
A PRIME 145
8.4.3 CHART OF 2-DIMENSIONAL
P
R
X
P
R
RTA 147
8.4.4 CASE
M = PQ, P
AND
Q
DISTINCT PRIMES 148
8.4.5 3-D REDUCED TRANSFORM ALGORITHMS 150
8.5 RTA PERMUTATIONS 152
BIBLIOGRAPGY 156
PROBLEMS 157
9 FIELD ALGORITHM 159
9.1 INTRODUCTION 159
9.2 RADER FIELD ALGORITHM 161
9.3 FINITE FIELDS 162
9.3.1 PROPERTIES OF FINITE FIELDS 162
9.3.2 EXAMPLES OF FINITE FIELDS 163
9.4 FOURIER TRANSFORM OF FINITE FIELDS . . 164
9.4.1 TRACE MAP 165
9.4.2 EVALUATION MAP 168
9.5 FACTORIZATION OF CORE MATRICES 169
9.6 AUSLANDER-FEIG-WINOGRAD DFT 173
BIBLIOGRAPGY 175
PROBLEMS 176
10 IMPLEMENTATION ON RISC ARCHITECTURES 179
10.1 INTRODUCTION 179
10.2 ALGORITHM DESIGN FOR RISC ARCHITECTURES 180
10.2.1 IMPLEMENTATION ON MODEL I RISC 182
10.2.2 IMPLEMENTATION ON MODEL II RISC 187
10.3 IMPLEMENTATION ON THE IBM RS/6000 189
10.4 IMPLEMENTATION ON THE INTEL I860 197
BIBLIOGRAPHY 200
YY
;
.
YYYY'YY
XII
CONTENTS
11 IMPLEMENTATION ON PARALLEL ARCHITECTURES 203
11.1 INTRODUCTION 203
11.2 PARALLEL IMPLEMENTATION OF FFT 206
11.3 PARALLEL IMPLEMENTATION OF THE RTA 207
11.3.1 2-DIMENSIONAL
P X P
CASE,
P
PRIME 208
11.4 NEW STRATEGY FOR THE PARALLEL IMPLEMENTATION OF FFT . . 210
11.5
HYBRID ALGORITHM 215
11.6 A PROGRAM EXAMPLE ON IPSC/860 219
BIBLIOGRAPHY 226
INDEX 231 |
| any_adam_object | 1 |
| author | Tolimieri, Richard 1940- An, Myoung Lu, Chao |
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| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| isbn | 3540941053 0387941053 |
| language | English |
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| physical | XIV, 233 S. |
| publishDate | 1993 |
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| spelling | Tolimieri, Richard 1940- Verfasser (DE-588)115626271 aut Mathematics of multidimensional Fourier transform algorithms Richard Tolimieri ; Myoung An ; Chao Lu New York [u.a.] Springer 1993 XIV, 233 S. txt rdacontent n rdamedia nc rdacarrier Signal processing and digital filtering Literaturangaben Algorithmes ram Fourier, Transformations de ram Transformation Fourier Fourier transformations Mehrdimensionale Datenstruktur (DE-588)4203964-2 gnd rswk-swf Fourier-Transformation (DE-588)4018014-1 gnd rswk-swf Fourier-Transformation (DE-588)4018014-1 s Mehrdimensionale Datenstruktur (DE-588)4203964-2 s DE-604 An, Myoung Verfasser aut Lu, Chao Verfasser aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006040558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tolimieri, Richard 1940- An, Myoung Lu, Chao Mathematics of multidimensional Fourier transform algorithms Algorithmes ram Fourier, Transformations de ram Transformation Fourier Fourier transformations Mehrdimensionale Datenstruktur (DE-588)4203964-2 gnd Fourier-Transformation (DE-588)4018014-1 gnd |
| subject_GND | (DE-588)4203964-2 (DE-588)4018014-1 |
| title | Mathematics of multidimensional Fourier transform algorithms |
| title_auth | Mathematics of multidimensional Fourier transform algorithms |
| title_exact_search | Mathematics of multidimensional Fourier transform algorithms |
| title_full | Mathematics of multidimensional Fourier transform algorithms Richard Tolimieri ; Myoung An ; Chao Lu |
| title_fullStr | Mathematics of multidimensional Fourier transform algorithms Richard Tolimieri ; Myoung An ; Chao Lu |
| title_full_unstemmed | Mathematics of multidimensional Fourier transform algorithms Richard Tolimieri ; Myoung An ; Chao Lu |
| title_short | Mathematics of multidimensional Fourier transform algorithms |
| title_sort | mathematics of multidimensional fourier transform algorithms |
| topic | Algorithmes ram Fourier, Transformations de ram Transformation Fourier Fourier transformations Mehrdimensionale Datenstruktur (DE-588)4203964-2 gnd Fourier-Transformation (DE-588)4018014-1 gnd |
| topic_facet | Algorithmes Fourier, Transformations de Transformation Fourier Fourier transformations Mehrdimensionale Datenstruktur Fourier-Transformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006040558&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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