The mathematics of signal processing:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2012
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge texts in applied mathematics
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024993392&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XII, 449 S. |
| ISBN: | 9781107013223 9781107601048 |
Internformat
MARC
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| 100 | 1 | |a Damelin, Steven B. |e Verfasser |0 (DE-588)185354823 |4 aut | |
| 245 | 1 | 0 | |a The mathematics of signal processing |c Steven B. Damelin ; Willard Miller |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2012 | |
| 300 | |a XII, 449 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-024993392 | |
Datensatz im Suchindex
| _version_ | 1819291558833291264 |
|---|---|
| adam_text | Contents
Preface
page
xi
Introduction
1
Normed vector spaces
3
1.1
Definitions
4
1.2
Inner products and norms
10
1.3
Finite-dimensional £p spaces
14
1.4
Digging deeper: completion of inner product spaces
20
1.5
Hubert spaces, L^ and
¿2 25
1.6
Orthogonal projections, Gram-Schmidt
orthogonalization
39
1.7
Linear operators and matrices, LS approximations
46
1.8
Additional exercises
64
Analytic tools
73
2.1
Improper integrals
73
2.2
The gamma functions and beta functions
78
2.3
The sine function and its improper relatives
79
2.4
Infinite products
83
2.5
Additional exercises
86
Fourier series
92
3.1
Definitions, real Fourier series and complex Fourier
series
92
3.2
Examples
96
3.3
Intervals of varying length, odd and even functions
97
3.4
Convergence results
99
3.5
More on pointwise convergence, Gibbs phenomena
107
3.6
Further properties of Fourier series
113
3.7
Digging deeper: arithmetic summability and
Fejér s
theorem
116
3.8
Additional exercises
123
The Fourier transform
127
4.1
Fourier transforms as integrals
127
4.2
The transform as a limit of Fourier series
129
4.3 ¿2
convergence of the Fourier transform
135
4.4
The Riemann-Lebesgue lemma and pointwise
convergence
140
4.5
Relations between Fourier series and integrals:
sampling
146
4.6
Fourier series and Fourier integrals: periodization
152
4.7
The Fourier integral and the uncertainty principle
154
4.8
Digging deeper
157
4.9
Additional exercises
161
Compressive
sampling
164
5.1
Introduction
164
5.2
Algebraic theory of
compressive
sampling
168
5.3
Analytic theory of
compressive
sampling
172
5.4
Probabilistic theory of
compressive
sampling
183
5.5
Discussion and practical implementation
201
5.6
Additional exercises
206
Discrete transforms
208
6.1
Z
transforms
208
6.2
Inverse
Z
transforms
211
6.3
Difference equations
213
6.4
Discrete Fourier transform and relations to Fourier
series
214
6.5
Fast Fourier transform (FFT)
222
6.6
Approximation to the Fourier transform
223
6.7
Additional exercises
224
Linear filters
230
7.1
Discrete linear filters
230
7.2
Continuous filters
233
7.3
Discrete filters in the frequency domain
235
7.4
Other operations on discrete signals
238
7.5
Additional exercises
240
Windowed Fourier and continuous
wavelet transforms. Frames
242
8.1
The windowed Fourier transform
243
8.2
Bases and frames,
windowed
frames
8.3 Affine
frames
8.4
Additional exercises
9
Multiresolution analysis
9.1
Haar
wavelets
9.2
The multiresolution structure
9.3
Filter banks and reconstruction of signals
9.4
The unitary two-channel filter bank system
9.5
A perfect reconstruction filter bank with JV
= 1
9.6
Perfect reconstruction for two-channel filter banks
9.7 Halfband
filters and spectral factorization
9.8
Maxflat filters
9.9
Low pass iteration and the cascade algorithm
9.10
Scaling functions by recursion: dyadic points
9.11
The cascade algorithm in the frequency domain
9.12
Some technical results
9.13
Additional exercises
10
Discrete wavelet theory
10.1
Li convergence
10.2
Accuracy of approximation
10.3
Smoothness of scaling functions and wavelets
10.4
Additional exercises
11 Biorthogonal
filters and wavelets
11.1
Resumé
of basic facts on
biorthogonal
filters
11.2 Biorthogonal
wavelets: multiresolution structure
11.3
Splines
11.4
Generalizations of filter banks and wavelets
11.5
Finite length signals
11.6
Circulant
matrices
11.7
Additional exercises
12
Parsimonious representation of data
12.1
The nature of digital images
12.2
Pattern recognition and clustering
12.3
Image representation of data
12.4
Image compression
12.5
Additional exercises
References
Index
|
| any_adam_object | 1 |
| author | Damelin, Steven B. Miller, Willard 1937- |
| author_GND | (DE-588)185354823 (DE-588)1022191268 |
| author_facet | Damelin, Steven B. Miller, Willard 1937- |
| author_role | aut aut |
| author_sort | Damelin, Steven B. |
| author_variant | s b d sb sbd w m wm |
| building | Verbundindex |
| bvnumber | BV040136335 |
| classification_rvk | ZN 6010 ZN 6025 |
| ctrlnum | (OCoLC)775825373 (DE-599)BVBBV040136335 |
| discipline | Elektrotechnik / Elektronik / Nachrichtentechnik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV040136335 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T16:08:56Z |
| institution | BVB |
| isbn | 9781107013223 9781107601048 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024993392 |
| oclc_num | 775825373 |
| open_access_boolean | |
| owner | DE-20 DE-739 DE-83 |
| owner_facet | DE-20 DE-739 DE-83 |
| physical | XII, 449 S. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series2 | Cambridge texts in applied mathematics |
| spellingShingle | Damelin, Steven B. Miller, Willard 1937- The mathematics of signal processing Signalverarbeitung (DE-588)4054947-1 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| subject_GND | (DE-588)4054947-1 (DE-588)4155620-3 |
| title | The mathematics of signal processing |
| title_auth | The mathematics of signal processing |
| title_exact_search | The mathematics of signal processing |
| title_full | The mathematics of signal processing Steven B. Damelin ; Willard Miller |
| title_fullStr | The mathematics of signal processing Steven B. Damelin ; Willard Miller |
| title_full_unstemmed | The mathematics of signal processing Steven B. Damelin ; Willard Miller |
| title_short | The mathematics of signal processing |
| title_sort | the mathematics of signal processing |
| topic | Signalverarbeitung (DE-588)4054947-1 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| topic_facet | Signalverarbeitung Mathematische Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024993392&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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