Discrete transforms:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Chapman & Hall
1992
|
| Edition: | 1. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 187 S. graph. Darst. |
| ISBN: | 041242990X 0442315945 |
Staff View
MARC
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| 245 | 1 | 0 | |a Discrete transforms |c Jean M. Firth |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a London [u.a.] |b Chapman & Hall |c 1992 | |
| 300 | |a XII, 187 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
| _version_ | 1804123169433321472 |
|---|---|
| adam_text | Contents
Acknowledgements ix
Preface x
1 Fourier series, integral theorem,
and transforms: a review 1
1.1 Fourier series 2
1.2 Fourier exponential series 3
1.3 The Fourier integral theorem 6
1.4 Odd and even functions 8
1.5 The Fourier transform 8
1.6 The Fourier sine and cosine transforms 11
1.7 The Laplace transform 11
1.8 Laplace transform properties and pairs 13
1.9 Transfer functions and convolution 19
Summary 21
Problems 21
2 The Fourier transform. Convolution of analogue signals 25
2.1 Duality 26
2.2 Further properties of the Fourier transform 28
2.3 Comparison with the Laplace transform, and the
existence of the Fourier transform 32
2.4 Transforming using a limit process 33
2.5 Transformation and inversion using duality
and other properties 35
2.6 Some frequently occurring functions
and their transforms 37
vi Contents
2.7 Further Fourier transform pairs 42
2.8 Graphical aspects of convolution 44
Summary 51
Problems 51
3 Discrete signals and transforms.
The Z transform and discrete convolution 54
3.1 Sampling, quantization and encoding 55
3.2 Sampling and ideal sampling models 56
3.3 The Fourier transform of a sampled function 57
3.4 The spectrum of an ideally sampled function 59
3.5 Aliasing 60
3.6 Transform and inversion sums; truncation 62
3.7 Windowing: band limited signals and signal energy 67
3.8 The Laplace transform of a sampled signal 72
3.9 The Z transform 72
3.10 Input output systems and transfer functions 74
3.11 Properties of the Z transform 75
3.12 Z transform pairs 78
3.13 Inversion 79
3.14 Discrete convolution 82
Summary 85
Problems 86
4 Difference equations and the Z transforms 91
4.1 Forward and backward difference operators 92
4.2 The approximation of a differential equation 92
4.3 Ladder networks 93
4.4 Bending in beams: trial methods of solution 94
4.5 Transforming a second order
forward difference equation 96
4.6 The characteristic polynomial and the
terms to be inverted 97
4.7 The case when the characteristic polynomial
has real roots 99
4.8 The case when the characteristic polynomial
has complex roots 101
4.9 The case when the characteristic equation has
repeated roots 105
4.10 Difference equations of order N 2 107
Contents vii
4.11 A backward difference equation 109
4.12 A second order equation:
comparison of the two methods 111
Summary 113
Problems 113
5 The discrete Fourier transform 117
5.1 Approximating the exponential Fourier series 118
5.2 Definition of the discrete Fourier transform 120
5.3 Establishing the inverse 121
5.4 Inversion by conjugation 126
5.5 Properties of the discrete Fourier transform 129
5.6 Discrete correlation 132
5.7 Parseval s theorem 133
5.8 A note on sampling in the frequency domain,
and a further comment on window functions 134
5.9 Computational effort and the
discrete Fourier transform 135
Summary 136
Problems 137
6 Simplification and factorization
of the discrete Fourier transform matrix 141
6.1 The coefficient matrix for an eight point
discrete Fourier transform 142
6.2 The permutation matrix and bit reversal 144
6.3 The output from four two point
discrete Fourier transforms 144
6.4 The output from two four point
discrete Fourier transforms 145
6.5 The output from an eight point
discrete Fourier transform 148
6.6 Butterfly calculations 151
6.7 Twiddle factors 152
6.8 Economies 154
Summary 154
Problems 155
viii Contents
7 Fast Fourier transforms 156
7.1 Fast Fourier transform algorithms 157
7.2 Decimation in time for an eight point
discrete Fourier transform: first stage 158
7.3 The second stage: further periodic aspects 159
7.4 The third stage 161
7.5 Construction of a flow graph 162
7.6 Inversion using the same decimation in time
signal flow graph 168
7.7 Decimation in frequency for an eight point
discrete Fourier transform 169
Summary 176
Problems 176
Appendix A: The Fourier integral theorem 178
Appendix B: The Hartley transform 180
Appendix C: Further reading 184
Index 185
|
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| author | Firth, Jean M. 1938- |
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| author_facet | Firth, Jean M. 1938- |
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| dewey-search | 515/.723 |
| dewey-sort | 3515 3723 |
| dewey-tens | 510 - Mathematics |
| discipline | Elektrotechnik Mathematik |
| edition | 1. ed. |
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| id | DE-604.BV008816497 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:25:30Z |
| institution | BVB |
| isbn | 041242990X 0442315945 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005832646 |
| oclc_num | 25026404 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-91 DE-BY-TUM DE-634 |
| physical | XII, 187 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Chapman & Hall |
| record_format | marc |
| spelling | Firth, Jean M. 1938- Verfasser (DE-588)1029488223 aut Discrete transforms Jean M. Firth 1. ed. London [u.a.] Chapman & Hall 1992 XII, 187 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analise funcional larpcal Transformations (Mathématiques) Transformations (Mathematics) Diskrete Fourier-Transformation (DE-588)4150175-5 gnd rswk-swf Diskrete Fourier-Transformation (DE-588)4150175-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005832646&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Firth, Jean M. 1938- Discrete transforms Analise funcional larpcal Transformations (Mathématiques) Transformations (Mathematics) Diskrete Fourier-Transformation (DE-588)4150175-5 gnd |
| subject_GND | (DE-588)4150175-5 |
| title | Discrete transforms |
| title_auth | Discrete transforms |
| title_exact_search | Discrete transforms |
| title_full | Discrete transforms Jean M. Firth |
| title_fullStr | Discrete transforms Jean M. Firth |
| title_full_unstemmed | Discrete transforms Jean M. Firth |
| title_short | Discrete transforms |
| title_sort | discrete transforms |
| topic | Analise funcional larpcal Transformations (Mathématiques) Transformations (Mathematics) Diskrete Fourier-Transformation (DE-588)4150175-5 gnd |
| topic_facet | Analise funcional Transformations (Mathématiques) Transformations (Mathematics) Diskrete Fourier-Transformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005832646&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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