Sampling theory: beyond bandlimited systems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2015
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXV, 810 S. Ill., graph. Darst. |
| ISBN: | 9781107003392 |
Internformat
MARC
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| 020 | |a 9781107003392 |9 978-1-107-00339-2 | ||
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| 040 | |a DE-604 |b ger |e aacr | ||
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| 100 | 1 | |a Eldar, Yonina C. |d 1973- |e Verfasser |0 (DE-588)1043849696 |4 aut | |
| 245 | 1 | 0 | |a Sampling theory |b beyond bandlimited systems |c Yonina C. Eldar |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2015 | |
| 300 | |a XXV, 810 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Signal processing |x Digital techniques |x Study and teaching (Higher) | |
| 650 | 4 | |a Signal processing |x Digital techniques |x Study and teaching (Graduate) | |
| 650 | 4 | |a Signal processing |x Statistical methods |x Study and teaching (Higher) | |
| 650 | 4 | |a Signal processing |x Statistical methods |x Study and teaching (Graduate) | |
| 650 | 4 | |a Sampling (Statistics) | |
| 650 | 0 | 7 | |a Signalverarbeitung |0 (DE-588)4054947-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Abtastung |0 (DE-588)4140375-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Abtastung |0 (DE-588)4140375-7 |D s |
| 689 | 0 | 1 | |a Signalverarbeitung |0 (DE-588)4054947-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027977381&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-027977381 | |
Datensatz im Suchindex
| DE-BY-862_location | 2000 |
|---|---|
| DE-BY-FWS_call_number | 2000/ZN 6025 E37 |
| DE-BY-FWS_katkey | 559512 |
| DE-BY-FWS_media_number | 083000512718 |
| _version_ | 1824553508523737089 |
| adam_text |
Contents
Preface page xvii
List of abbreviations xxiv
1 Introduction 1
1.1 Standard sampling 2
1.2 Beyond bandlimited signals 5
1.3 Outline and outlook 6
2 Introduction to linear algebra 9
2.1 Signal expansions: some examples 9
2.2 Vector spaces 13
2.2.1 Subspaces 13
2.2.2 Properties of subspaces 14
2.3 Inner product spaces 15
2.3.1 The inner product 16
2.3.2 Orthogonality 17
2.3.3 Calculus in inner product spaces 19
2.3.4 Hilbert spaces 20
2.4 Linear transformations 21
2.4.1 Subspaces associated with a linear transformation 22
2.4.2 Invertibility 24
2.4.3 Direct-sum decompositions 25
2.4.4 The adjoint 29
2.5 Basis expansions 32
2.5.1 Set transformations 33
2.5.2 Bases 35
2.5.3 Riesz bases 36
2.5.4 Riesz basis expansions 40
2.6 Projection operators 44
2.6.1 Orthogonal projection operators 46
2.6.2 Oblique projection operators 48
2.7 Pseudoinverse of a transformation 51
2.7.1 Definition and properties 52
2.7.2 Matrices 54
Contents
viii
2.8 Frames 55
2.8.1 Definition of frames 56
2.8.2 Frame expansions 58
2.8.3 The canonical dual 59
2.9 Exercises 63
Fourier analysis 67
3.1 Linear time-invariant systems 68
3.1.1 Linearity and time-invariance 68
3.1.2 The impulse response 71
3.1.3 Causality and stability 73
3.1.4 Eigenfunctions of LTI systems 75
3.2 The continuous-time Fourier transform 75
3.2.1 Definition of the CTFT 75
3.2.2 Properties of the CTFT 76
3.2.3 Examples of the CTFT 77
3.2.4 Fubini’s theorem 79
3.3 Discrete-time systems 80
3.3.1 Discrete-time impulse response 80
3.3.2 Discrete-time Fourier transform 81
3.3.3 Properties of the DTFT 82
3.4 Continuous-discrete representations 85
3.4.1 Poisson-sum formula 87
3.4.2 Sampled correlation sequences 88
3.5 Exercises 90
Signal spaces 95
4.1 Structured bases 95
4.1.1 Sampling and reconstruction spaces 95
4.1.2 Practical sampling theorems 96
4.2 Bandlimited sampling 98
4.2.1 The Shannon-Nyquist theorem 98
4.2.2 Sampling by modulation 100
4.2.3 Aliasing 102
4.2.4 Orthonormal basis interpretation 105
4.2.5 Towards more general sampling spaces 109
4.3 Sampling in shift-invariant spaces 110
4.3.1 Shift-invariant spaces 110
4.3.2 Spline functions 112
4,3.3 Digital communication signals 114
4.3.4 Multiple generators 117
4.3.5 Refinable functions 121
Contents
ix
4.4 Gabor and wavelet expansions 122
4.4.1 Gabor spaces 122
4.4.2 Wavelet expansions 126
4.5 Union of subspaces 132
4.5.1 Signal model 133
4.5.2 Union classes 136
4.6 Stochastic and smoothness priors 138
4.7 Exercises 142
Shift-invariant spaces 146
5.1 Riesz basis in SI spaces 146
5.1.1 Riesz basis condition 147
5.1.2 Examples 149
5.2 Riesz basis expansions 152
5.2.1 Biorthogonal basis 152
5.2.2 Expansion coefficients 155
5.2.3 Alternative basis expansions 156
5.3 Partition of unity 161
5.4 Redundant sampling in SI spaces 163
5.4.1 Redundant bandlimited sampling 165
5.4.2 Missing samples 168
5.5 Multiple generators 169
5.5.1 Riesz condition 170
5.5.2 Biorthogonal basis 171
5.6 Exercises 175
Subspace priors 178
6.1 Sampling and reconstruction processes 178
6.1.1 Sampling setups 178
6.1.2 Sampling process 179
6.1.3 Unconstrained recovery 181
6.1.4 Predefined recovery kernel 182
6.1.5 Design objectives 183
6.2 Unconstrained reconstruction 186
6.2.1 Geometric interpretation 186
6.2.2 Equal sampling and prior spaces 188
6.3 Sampling in general spaces 191
6.3.1 The direct-sum condition 192
6.3.2 Unique recovery 194
6.3.3 Computing the oblique projection operator 198
6,3.4 Oblique biorthogonal basis 202
6.4 Summary: unique unconstrained recovery 205
6.4.1 Consistent recovery 205
6.4.2 Recovery error 208
X
Contents
6.5 Nonunique recovery 211
6.5.1 Least squares recovery 211
6.5.2 Minimax recovery 213
6.6 Constrained recovery 215
6.6.1 Minimal-error recoveiy 216
6.6.2 Least squares recovery 219
6.6.3 Minimax recovery 222
6.7 Unified formulation of recovery techniques 224
6.8 Multichannel sampling 226
6.8.1 Recovery methods 226
6.8.2 Papoulis’ generalized sampling 227
6.9 Exercises 235
Smoothness priors 238
7.1 Unconstrained recovery 238
7.1.1 Smoothness prior 238
7.1.2 Least squares solution 239
7.1.3 Minimax solution 242
7.1.4 Examples 243
7.1.5 Multichannel sampling 247
7.2 Constrained recovery 249
7.2.1 Least squares solution 249
7.2.2 Minimax-regret solution 251
7.2.3 Comparison between least squares and minimax 256
7.3 Stochastic priors 259
7.3.1 The hybrid Wiener filter 261
7.3.2 Constrained reconstruction 263
7.4 Summary of sampling methods 265
7.4.1 Summary of methods 265
7.4.2 Unified view 268
7.5 Sampling with noise 269
7.5.1 Constrained reconstruction problem 270
7.5.2 Least squares solution 272
7.5.3 Regularized least squares 273
7.5.4 Minimax MSE filters 273
7.5.5 Hybrid Wiener filter 275
7.5.6 Summary of the different filters 275
7.5.7 Bandlimited interpolation 277
7.5.8 Unconstrained recovery 279
7.6 Exercises 281
Contents
XI
Nonlinear sampling 284
8.1 Sampling with nonlinearities 285
8.1.1 Nonlinear model 285
8.1.2 Wiener-Hammerstein systems 286
8.2 Pointwise sampling 288
8.2.1 Bandlimited signals 288
8.2.2 Reproducing kernel Hilbert spaces 290
8.3 Subspace-preserving nonlinearities 294
8.4 Equal prior and sampling spaces 295
8.4.1 Iterative recovery 297
8.4.2 Linearization approach 302
8.4.3 Conditions for invertibility 305
8.4.4 Newton algorithm 306
8.4.5 Comparison between algorithms 310
8.5 Arbitrary sampling filters 312
8.5.1 Recovery algorithms 312
8.5.2 Uniqueness conditions 314
8.5.3 Algorithm convergence 317
8.5.4 Examples 319
8.6 Exercises 322
Resampling 325
9.1 Bandlimited sampling rate conversion 326
9.1.1 Interpolation by an integer factor I 327
9.1.2 Decimation by an integer factor D 329
9.1.3 Rate conversion by a rational factor I/D 332
9.1.4 Rate conversion by arbitrary factors 334
9.2 Spline interpolation 337
9.2.1 Interpolation formula 337
9.2.2 Comparison with bandlimited interpolation 340
9.3 Dense-grid interpolation 341
9.3.1 Sub space prior 342
9.3.2 Smoothness prior 348
9.3.3 Stochastic prior 349
9.4 Projection-based resampling 350
9.4.1 Orthogonal projection resampling 351
9.4.2 Oblique projection resampling 357
9.5 Summary of conversion methods 365
9.5.1 Computational aspects 365
9.5.2 Anti-aliasing aspects 366
9.6 Exercises 366
370
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Contents
Union of subspaces
10.1 Motivating examples
10.1.1 Multiband sampling
10.1.2 Time-delay estimation
10.2 Union model
10.2.1 Definition and properties
10.2.2 Classes of unions
10.3 Sampling over unions
10.3.1 Unique and stable sampling
10.3.2 Rate requirements
10.3.3 Xampling: compressed sampling methods
10.4 Exercises
Compressed sensing
11.1 Motivation for compressed sensing
11.2 Sparsity models
11.2.1 Normed vector spaces
11.2.2 Sparse signal models
11.2.3 Low-rank matrix models
11.3 Sensing matrices
11.3.1 Null space conditions
11.3.2 The restricted isometry property
11.3.3 Coherence
11.3.4 Uncertainty relations
11.3.5 Sensing matrix constructions
11.4 Recovery algorithms
11.4.1 ^recovery
11.4.2 Greedy algorithms
11.4.3 Combinatorial algorithms
11.4.4 Analysis versus synthesis methods
11.5 Recovery guarantees
11.5.1 £i recovery: RIP-based results
11.5.2 t\ recovery: coherence-based results
11.5.3 Instance-optimal guarantees
11.5.4 The cross-poly tope and phase transitions
11.5.5 Guarantees on greedy methods
11.6 Multiple measurement vectors
11.6.1 Signal model
11.6.2 Recovery algorithms
11.6.3 Performance guarantees
11.6.4 Infinite measurement vectors
11.7 Summary and extensions
11.8 Exercises
Contents
xiii
12 Sampling over finite unions 475
12.1 Finite unions 475
12.1.1 Signal model 475
12.1.2 Problem formulation 47 8
12.1.3 Connection with block sparsity 479
12.2 Uniqueness and stability 482
12.2.1 Block RIP 483
12.2.2 Block coherence and subcoherence 485
12.3 Signal recovery algorithms 488
12.3.1 Exponential recovery algorithm 488
12.3.2 Convex recovery algorithm 489
12.3.3 Greedy algorithms 490
12.4 RIP-based recovery results 493
12.4.1 Block basis pursuit recovery 493
12.4.2 Random matrices and block RIP 499
12.5 Coherence-based recovery results 500
12.5.1 Recovery conditions 500
12.5.2 Extensions 504
12.5.3 Proofs of theorems 507
12.6 Dictionary and subspace learning 513
12.6.1 Dictionary learning 514
12.6.2 Subspace learning 517
12.7 Blind compressed sensing 522
12.7.1 BCS problem formulation 522
12.7.2 BCS with a constrained dictionary 523
12.7.3 BCS with multiple measurement matrices 531
12.8 Exercises 534
13 Sampling over shift-invariant unions 539
13.1 Union model 539
13.1.1 Sparse union of SI subspaces 539
13.1.2 Sub-Nyquist sampling 541
13.2 Compressed sensing in sparse unions 543
13.2.1 Union of discrete sequences 543
13.2.2 Reduced-rate sampling 545
13.3 Application to detection 553
13.3.1 Matched-filter receiver 554
13.3.2 Maximum-likelihood detector 556
13.3.3 Compressed-sensing receiver 557
13.4 Multiuser detection 563
13.4.1 Conventional multiuser detectors 564
13.4.2 Reduced-dimension MUD (RD-MUD) 565
13.4.3 Performance of RD-MUD 568
13.5 Exercises 571
574
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682
Contents
Multiband sampling
14.1 Sampling of multiband signals
14.2 Multiband signals with known carriers
14.2.1 HQ demodulation
14.2.2 Landau rate
14.2.3 Direct undersampling of bandpass signals
14.3 Interleaved ADCs
14.3.1 Bandpass sampling
14.3.2 Multiband sampling
14.3.3 Universal sampling patterns
14.3.4 Hardware considerations
14.4 Modulated wideband converter
14.4.1 MWC operation
14.4.2 MWC signal recovery
14.4.3 Collapsing channels
14.4.4 Sign-alternating sequences
14.5 Blind sampling of multiband signals
14.5.1 Minimal sampling rate
14.5.2 Blind recovery
14.5.3 Multicoset sampling and the sparse SI framework
14.5.4 Sub-Nyquist baseband processing
14.5.5 Noise folding
14.6 Hardware prototype of sub-Nyquist multiband sensing
14.7 Simulations
14.7.1 MWC designs
14.7.2 Sign-alternating sequences
14.7.3 Effect of CTF length
14.7.4 Parameter limits
14.8 Exercises
Finite rate of innovation sampling
15.1 Finite rate of innovation signals
15.1.1 Shift-invariant spaces
15.1.2 Channel sounding
15.1.3 Other examples
15.2 Periodic pulse streams
15.2.1 Time-domain formulation
15.2.2 Frequency-domain formulation
15.2.3 Prony’s method
15.2.4 Noisy samples
15.2.5 Matrix pencil
15.2.6 Subspace methods
15.2.7 Covariance-based methods
Contents
XV
15.2.8 Compressed sensing formulation 686
15.2.9 Sub-Nyquist sampling 688
15.3 Sub-Nyquist sampling with a single channel 692
15.3.1 Coset sampling 692
15.3.2 Sum-of-sincs filter 695
15.3.3 Noise effects 698
15.3.4 Finite and infinite pulse streams 701
15.4 Multichannel sampling 705
15.4.1 Modulation-based multichannel systems 706
15.4.2 Filterbank sampling 714
15.5 Noisy FRI recovery 717
15.5.1 MSE bounds 718
15.5.2 Periodic versus semiperiodic FRI signals 721
15.5.3 Choosing the sampling kernels 723
15.6 General FRI sampling 723
15.6.1 Sampling method 724
15.6.2 Minimal sampling rate 725
15.6.3 Least squares recovery 727
15.6.4 Iterative recovery 728
15.7 Applications of FRI 733
15.7.1 Sub-Nyquist radar 733
15.7.2 Time-varying system identification 743
15.7.3 Ultrasound imaging 744
15.8 Exercises 750
Appendix A Finite linear algebra 755
A.l Matrices 755
A. 1.1 Matrix operations 755
A. 1.2 Matrix properties 756
A. 1.3 Special classes of matrices 758
A.2 Eigendecomposition of matrices 760
A.2.1 Eigenvalues and eigenvectors 760
A.2.2 Singular value decomposition 763
A.3 Linear equations 764
A. 4 Matrix norms 765
A.4.1 Induced norms 766
A. 4.2 Entry wise norms 767
A. 4.3 Schatten norms 767
Appendix B Stochastic signals 768
B. 1 Random variables 768
B. 1.1 Probability density function 768
B. 1.2 Jointly random variables 769
B.2 Random vectors 770
xvi
Contents
B.3 Random processes 770
B.3.1 Continuous-time random processes 770
B.3.2 Discrete-time random processes 772
B.4 Sampling of bandlimited processes 773
References 775
Index 799 |
| any_adam_object | 1 |
| author | Eldar, Yonina C. 1973- |
| author_GND | (DE-588)1043849696 |
| author_facet | Eldar, Yonina C. 1973- |
| author_role | aut |
| author_sort | Eldar, Yonina C. 1973- |
| author_variant | y c e yc yce |
| building | Verbundindex |
| bvnumber | BV042543356 |
| callnumber-first | T - Technology |
| callnumber-label | TK5102 |
| callnumber-raw | TK5102.9 |
| callnumber-search | TK5102.9 |
| callnumber-sort | TK 45102.9 |
| callnumber-subject | TK - Electrical and Nuclear Engineering |
| classification_rvk | SK 840 ZN 6025 |
| classification_tum | MAT 629f |
| ctrlnum | (OCoLC)911060158 (DE-599)BVBBV042543356 |
| dewey-full | 621.382/23 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 621 - Applied physics |
| dewey-raw | 621.382/23 |
| dewey-search | 621.382/23 |
| dewey-sort | 3621.382 223 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV042543356 |
| illustrated | Illustrated |
| indexdate | 2025-02-20T06:36:59Z |
| institution | BVB |
| isbn | 9781107003392 |
| language | English |
| lccn | 014014930 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027977381 |
| oclc_num | 911060158 |
| open_access_boolean | |
| owner | DE-862 DE-BY-FWS DE-83 DE-91G DE-BY-TUM DE-739 DE-29T DE-706 |
| owner_facet | DE-862 DE-BY-FWS DE-83 DE-91G DE-BY-TUM DE-739 DE-29T DE-706 |
| physical | XXV, 810 S. Ill., graph. Darst. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spellingShingle | Eldar, Yonina C. 1973- Sampling theory beyond bandlimited systems Signal processing Digital techniques Study and teaching (Higher) Signal processing Digital techniques Study and teaching (Graduate) Signal processing Statistical methods Study and teaching (Higher) Signal processing Statistical methods Study and teaching (Graduate) Sampling (Statistics) Signalverarbeitung (DE-588)4054947-1 gnd Abtastung (DE-588)4140375-7 gnd |
| subject_GND | (DE-588)4054947-1 (DE-588)4140375-7 |
| title | Sampling theory beyond bandlimited systems |
| title_auth | Sampling theory beyond bandlimited systems |
| title_exact_search | Sampling theory beyond bandlimited systems |
| title_full | Sampling theory beyond bandlimited systems Yonina C. Eldar |
| title_fullStr | Sampling theory beyond bandlimited systems Yonina C. Eldar |
| title_full_unstemmed | Sampling theory beyond bandlimited systems Yonina C. Eldar |
| title_short | Sampling theory |
| title_sort | sampling theory beyond bandlimited systems |
| title_sub | beyond bandlimited systems |
| topic | Signal processing Digital techniques Study and teaching (Higher) Signal processing Digital techniques Study and teaching (Graduate) Signal processing Statistical methods Study and teaching (Higher) Signal processing Statistical methods Study and teaching (Graduate) Sampling (Statistics) Signalverarbeitung (DE-588)4054947-1 gnd Abtastung (DE-588)4140375-7 gnd |
| topic_facet | Signal processing Digital techniques Study and teaching (Higher) Signal processing Digital techniques Study and teaching (Graduate) Signal processing Statistical methods Study and teaching (Higher) Signal processing Statistical methods Study and teaching (Graduate) Sampling (Statistics) Signalverarbeitung Abtastung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027977381&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT eldaryoninac samplingtheorybeyondbandlimitedsystems |
Inhaltsverzeichnis
THWS Schweinfurt Zentralbibliothek Lesesaal
| Signatur: |
2000 ZN 6025 E37 |
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| Exemplar 1 | ausleihbar Verfügbar Bestellen |