Mathematics of multidimensional Fourier transform algorithms:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
New York [u.a.]
Springer
1997
|
| Edition: | 2. ed. |
| Series: | Signal processing and digital filtering
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 187 S. graph. Darst. |
| ISBN: | 0387982604 |
Staff View
MARC
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Record in the Search Index
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| adam_text |
RICHARD TOLIMIERI MYOUNG AN CHAO LU
MATHEMATICS OF
MULTIDIMENSIONAL
FOURIER
TRANSFORM
ALGORITHMS
SECOND
EDITION
C.S. BURRUS
CONSULTING
EDITOR
WITH 21 ILLUSTRATIONS
SPRINGER
CONTENTS
PREFACE
TENSOR PRODUCT 1
1.1 INTRODUCTION 1
1.2 TENSOR PRODUCT 2
1.3 STRIDE PERMUTATIONS 6
1.4 ALGEBRA OF STRIDE PERMUTATIONS 8
1.5 TENSOR PRODUCT FACTORIZATION 10
1.6 FAST FOURIER TRANSFORM ALGORITHMS I 13
1.7 GENERAL 1-DIMENSIONAL FFT 16
REFERENCES 20
PROBLEMS 23
MULTIDIMENSIONAL TENSOR PRODUCT AND FFT 25
2.1 INTRODUCTION 25
2.2 MULTIDIMENSIONAL FOURIER TRANSFORM 26
2.3 2-DIMENSIONAL OPERATIONS 28
2.4 2-DIMENSIONAL COOLEY-TUKEY FFT 32
REFERENCES 35
PROBLEMS 36
FINITE ABELIAN GROUPS 37
3.1 INTRODUCTION 37
3.2 CHARACTER GROUP 39
CONTENTS
3.3 DUALITY 42
3.4 CHINESE REMAINDER THEOREM 44
3.5 VECTOR SPACE
L(A)
48
REFERENCES 49
PROBLEMS 49
FOURIER TRANSFORM OF FINITE ABELIAN GROUPS 51
4.1 INTRODUCTION 51
4.2 FOURIER TRANSFORM OF
A
51
4.3 INDUCED FOURIER TRANSFORM 53
4.4 PERIODIC AND DECIMATED DATA 55
4.5 PERIODIZATION AND DECIMATION 57
REFERENCES 61
COOLEY-TUKEY AND GOOD-THOMAS 63
5.1 INTRODUCTION 63
5.2 GOOD-THOMAS FFT 64
5.3 ABSTRACT COOLEY-TUKEY FFT 65
REFERENCES 69
LINES 71
6.1 INTRODUCTION 71
6.2 EXAMPLES 72
6.3 PRIME CASE 75
6.4 PRIME POWER CASE 76
6.4.1 SQUARE CASE 76
6.4.2 RECTANGULAR CASE 81
6.5 GENERAL SQUARE CASE 84
6.6 GENERAL RECTANGULAR CASE 87
REFERENCES 88
PROBLEMS 89
DUALITY OF LINES AND PLANES 91
7.1 AUTOMORPHISM GROUP 91
7.2 DUAL OF LINES 94
7.3 PLANES 97
7.4 DUALITY 99
REFERENCES 103
PROBLEMS 103
REDUCED TRANSFORM ALGORITHMS 105
8.1 INTRODUCTION 105
8.2 GENERAL STRUCTURE 106
8.3 PERIODIZATIONS 108
8.4 EXAMPLES ILL
CONTENTS XI
8.4.1 2-DIMENSIONAL
P
X
P, P
A PRIME ILL
8.4.2
2-DIMENSIONAL
P
2
X P
2
,
P
A PRIME 113
8.4.3 2-DIMENSIONAL
P
R
X
P
R
RTA 116
8.4.4 2-DIMENSIONAL
M =
PQ,
P
AND
Q
DISTINCT PRIMES . . 116
8.4.5
3-D RTA 118
8.5 RTA PERMUTATIONS 120
REFERENCES 123
PROBLEMS 123
9 FIELD ALGORITHM 125
9.1 INTRODUCTION 125
9.2 RADER FIELD ALGORITHM 126
9.3 FINITE FIELDS 128
9.3.1 PROPERTIES OF FINITE FIELDS 128
9.3.2 EXAMPLES OF FINITE FIELDS 128
9.4 FOURIER TRANSFORM OF FINITE FIELDS 129
9.4.1 TRACE MAP 130
9.4.2 EVALUATION MAP 132
9.5 FACTORIZATION OF CORE MATRICES 133
9.6 AUSLANDER-FEIG-WINOGRAD DFT 137
REFERENCES 138
PROBLEMS 139
10 IMPLEMENTATION ON RISC ARCHITECTURES 141
10.1 INTRODUCTION 141
10.2 ALGORITHMS FOR RISC ARCHITECTURES 142
10.2.1 IMPLEMENTATION ON MODEL I RISC 143
10.2.2 IMPLEMENTATION ON MODEL II RISC 147
10.3 IMPLEMENTATION ON THE IBM RS/6000 149
10.4 IMPLEMENTATION ON THE INTEL I860 156
REFERENCES 159
11 IMPLEMENTATION ON PARALLEL ARCHITECTURES 161
11.1 INTRODUCTION 161
11.2 PARALLEL IMPLEMENTATION OF FFT 163
11.3 PARALLEL IMPLEMENTATION OF THE RTA 164
11.3.1 2-DIMENSIONAL PRIME CASE 165
11.4 PARALLEL IMPLEMENTATION OF FFT 166
11.5 HYBRID ALGORITHM 170
11.6 AN EXAMPLE PROGRAM ON IPSC/860 173
REFERENCES 180
INDEX 185 |
| any_adam_object | 1 |
| author | Tolimieri, Richard 1940- An, Myoung Lu, Chao |
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| author_facet | Tolimieri, Richard 1940- An, Myoung Lu, Chao |
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| classification_rvk | SK 450 |
| ctrlnum | (OCoLC)36760486 (DE-599)BVBBV011554163 |
| dewey-full | 515/.723 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.723 |
| dewey-search | 515/.723 |
| dewey-sort | 3515 3723 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2025-03-10T13:03:03Z |
| institution | BVB |
| isbn | 0387982604 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007779518 |
| oclc_num | 36760486 |
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| owner | DE-703 DE-473 DE-BY-UBG |
| owner_facet | DE-703 DE-473 DE-BY-UBG |
| physical | XI, 187 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| series2 | Signal processing and digital filtering |
| spelling | Tolimieri, Richard 1940- Verfasser (DE-588)115626271 aut Mathematics of multidimensional Fourier transform algorithms Richard Tolimieri ; Myoung An ; Chao Lu. 2. ed. New York [u.a.] Springer 1997 XI, 187 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Signal processing and digital filtering 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=007779518&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 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 | Fourier transformations Mehrdimensionale Datenstruktur (DE-588)4203964-2 gnd Fourier-Transformation (DE-588)4018014-1 gnd |
| topic_facet | Fourier transformations Mehrdimensionale Datenstruktur Fourier-Transformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007779518&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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