Quaternion Fourier transforms for signal and image processing:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
ISTE [u.a.]
2014
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| Schriftenreihe: | Focus series
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 127 S. Ill., graph. Darst. |
| ISBN: | 9781848214781 |
Internformat
MARC
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| 245 | 1 | 0 | |a Quaternion Fourier transforms for signal and image processing |c Todd A. Ell ; Nicolas Le Bihan ; Stephen J. Sangwine |
| 264 | 1 | |a London [u.a.] |b ISTE [u.a.] |c 2014 | |
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Datensatz im Suchindex
| _version_ | 1804152418977447936 |
|---|---|
| adam_text | Titel: Quaternion Fourier transforms for signal and image processing
Autor: Ell, Todd A
Jahr: 2014
Contents
NOMENCLATURE .................................. ix
PREFACE ....................................... Xi
Introduction ................................... xiü
Chapter 1. Quaternion Algebra ..................... 1
1.1. Definitions .................................. 1
1.2. Properties................................... 2
1.3. Exponential and logarithmofa quaternion ................ 7
1.3.1. Exponential ofa pure quaternion.................... 7
1.3.2. Exponential ofa füll quaternion.................... 9
1.3.3. Logarithm of a quaternion........................ 10
1.4. Representations................................ 11
1.4.1. Polar forms................................ 11
1.4.2. The C^-pair notation........................... 15
1.4.3. RandC matrix representations..................... 17
1.5. Powers of a quaternion............................ 18
1.6. Subfields ................................... 18
Chapter 2. Geometric Applications................... 21
2.1. Euclidean geometry (3D and 4D)...................... 21
2.1.1. 3D reflections............................... 22
2.1.2. 3D rotations................................ 22
2.1.3. 3D shears................................. 24
2.1.4. 3D dilations................................ 24
vi Quaternion Fourier Transforms for Signal and Image Processing
2.1.5. 4D reflections............................... 25
2.1.6. 4D rotations................................ 25
2.2. Spherical geometry.............................. 26
2.3. Projective space (3D) ............................ 28
2.3.1. Systems of linear quaternion funetions ................ 31
2.3.2. Projective transformations........................ 33
Chapter 3. Quaternion Fourier Transforms ............ 35
3.1. 1D quaternion Fourier transforms ..................... 38
3.1.1. Definitions ................................ 38
3.1.2. Basic transform pairs .......................... 40
3.1.3. Decompositions ............................. 42
3.1.4. Inter-relationships between definitions................. 45
3.1.5. Convolution and correlation theorems................. 47
3.2. 2D quaternion Fourier transforms ..................... 48
3.2.1. Definitions ................................ 48
3.2.2. Basic transform pairs .......................... 52
3.2.3. Decompositions ............................. 54
3.2.4. Inter-relationships between definitions................. 55
3.3. Computational aspects............................ 57
3.3.1. Coding .................................. 57
3.3.2. Verification................................ 62
3.3.3. Verification of transforms........................ 62
Chapter 4. Signal and Image Processing ............... 67
4.1. Generalized convolution........................... 67
4.1.1. Classical grayscale image convolution Alters............. 67
4.1.2. Colorimages as quaternion arrays................... 70
4.1.3. Quaternion convolution......................... 70
4.1.4. Quaternion image spectrum....................... 73
4.2. Generalized correlation........................... 79
4.2.1. Classical correlation and phase correlation.............. 81
4.2.2. Quaternion correlation.......................... 86
4.2.3. Quaternion phase correlation...................... 88
4.3. Instantaneous phase and amplitude of complex Signals ......... 91
4.3.1. Important properties of 1DQFT ofa complex signal z(t)...... 91
4.3.2. Hubert transform and right-sided quaternion spectrum ....... 96
4.3.3. The quaternion signal associated with a complex signal....... 98
4.3.4. Instantaneous amplitude and phase................... 101
4.3.5. The instantaneous frequency ofa complex signal........... 102
Contents vii
4.3.6. Examples................................. 104
4.3.7. The quaternion Wigner-Ville distribution ofa complex signal . . . 109
4.3.8. Time marginal.............................. 113
4.3.9. The mean frequency formula...................... 113
Bibliography ................................... 117
Index......................................... 123
|
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| author | Ell, Todd A. Le Bihan, Nicolas Sangwine, Stephen J. 1956- |
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| author_sort | Ell, Todd A. |
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| bvnumber | BV042005986 |
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| ctrlnum | (OCoLC)915532181 (DE-599)HBZHT018208818 |
| discipline | Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
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| id | DE-604.BV042005986 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:10:24Z |
| institution | BVB |
| isbn | 9781848214781 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027447930 |
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| owner_facet | DE-83 |
| physical | XXII, 127 S. Ill., graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | ISTE [u.a.] |
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| series2 | Focus series |
| spelling | Ell, Todd A. Verfasser (DE-588)1051890640 aut Quaternion Fourier transforms for signal and image processing Todd A. Ell ; Nicolas Le Bihan ; Stephen J. Sangwine London [u.a.] ISTE [u.a.] 2014 XXII, 127 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Focus series Fourier-Transformation (DE-588)4018014-1 gnd rswk-swf Signalverarbeitung (DE-588)4054947-1 gnd rswk-swf Bildverarbeitung (DE-588)4006684-8 gnd rswk-swf Quaternion (DE-588)4176653-2 gnd rswk-swf Fourier-Transformation (DE-588)4018014-1 s Quaternion (DE-588)4176653-2 s Signalverarbeitung (DE-588)4054947-1 s Bildverarbeitung (DE-588)4006684-8 s DE-604 Le Bihan, Nicolas Verfasser (DE-588)1051891019 aut Sangwine, Stephen J. 1956- Verfasser (DE-588)1051891426 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027447930&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ell, Todd A. Le Bihan, Nicolas Sangwine, Stephen J. 1956- Quaternion Fourier transforms for signal and image processing Fourier-Transformation (DE-588)4018014-1 gnd Signalverarbeitung (DE-588)4054947-1 gnd Bildverarbeitung (DE-588)4006684-8 gnd Quaternion (DE-588)4176653-2 gnd |
| subject_GND | (DE-588)4018014-1 (DE-588)4054947-1 (DE-588)4006684-8 (DE-588)4176653-2 |
| title | Quaternion Fourier transforms for signal and image processing |
| title_auth | Quaternion Fourier transforms for signal and image processing |
| title_exact_search | Quaternion Fourier transforms for signal and image processing |
| title_full | Quaternion Fourier transforms for signal and image processing Todd A. Ell ; Nicolas Le Bihan ; Stephen J. Sangwine |
| title_fullStr | Quaternion Fourier transforms for signal and image processing Todd A. Ell ; Nicolas Le Bihan ; Stephen J. Sangwine |
| title_full_unstemmed | Quaternion Fourier transforms for signal and image processing Todd A. Ell ; Nicolas Le Bihan ; Stephen J. Sangwine |
| title_short | Quaternion Fourier transforms for signal and image processing |
| title_sort | quaternion fourier transforms for signal and image processing |
| topic | Fourier-Transformation (DE-588)4018014-1 gnd Signalverarbeitung (DE-588)4054947-1 gnd Bildverarbeitung (DE-588)4006684-8 gnd Quaternion (DE-588)4176653-2 gnd |
| topic_facet | Fourier-Transformation Signalverarbeitung Bildverarbeitung Quaternion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027447930&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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