Foundations of signal processing:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2014
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXVII, 715 S. Ill., graph. Darst. |
| ISBN: | 9781107038608 |
Internformat
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| 245 | 1 | 0 | |a Foundations of signal processing |c Martin Vetterli, Jelena Kovaěvić, Vivek K. Goyal |
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| 300 | |a XXVII, 715 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804152534308225024 |
|---|---|
| adam_text | Titel: Foundations of signal processing
Autor: Vetterli, Martin
Jahr: 2014
Contents
Quick reference page xvii
Acknowledgments xxiii
Preface xxv
1 On rainbows and spectra 1
2 From Euclid to Hubert 9
2.1 Introduction 10
2.2 Vector spaces 18
2.2.1 Definition and properties 18
2.2.2 Inner product 23
2.2.3 Norm 27
2.2.4 Standard spaces 30
2.3 Hubert spaces 35
2.3.1 Convergence 36
2.3.2 Completeness 37
2.3.3 Linear operators 40
2.4 Approximations, projections, and decompositions 50
2.4.1 Projection theorem 51
2.4.2 Projection operators 54
2.4.3 Direct sums and subspace decompositions 60
2.4.4 Minimum mean-squared error estimation 63
2.5 Bases and frames 69
2.5.1 Bases and Riesz bases 69
2.5.2 Orthonormal bases 76
2.5.3 Biorthogonal pairs of bases 86
2.5.4 Frames 101
2.5.5 Matrix representations of vectors and linear operators 109
2.6 Computational aspects 119
2.6.1 Cost, complexity, and asymptotic notations 120
2.6.2 Precision 123
2.6.3 Conditioning 126
2.6.4 Solving systems of linear equations 129
2. A Elements of analysis and topology 135
2.A.1 Basic definitions 135
XI
xii Contents
2.A.2 Convergence 136
2.A.3 Interchange theorems 138
2.A.4 Inequalities 139
2.A.5 Integration by parts 140
2.B Elements of linear algebra 141
2.B.1 Basic definitions and properties 141
2.B.2 Special matrices 147
2.C Elements of probability 151
2.C.1 Basic definitions 151
2.C.2 Standard distributions 154
2.C.3 Estimation 155
2.D Basis concepts 159
Chapter at a glance 161
Historical remarks 162
Further reading 162
Exercises with solutions 163
Exercises 169
3 Sequences and discrete-time systems 181
3.1 Introduction 182
3.2 Sequences 185
3.2.1 Infinite-length sequences 185
3.2.2 Finite-length sequences 192
3.2.3 Two-dimensional sequences 193
3.3 Systems 195
3.3.1 Discrete-time systems and their properties 195
3.3.2 Difference equations 202
3.3.3 Linear shift-invariant systems 205
3.4 Discrete-time Fourier transform 216
3.4.1 Definition of the DTFT 216
3.4.2 Existence and convergence of the DTFT 218
3.4.3 Properties of the DTFT 221
3.4.4 Frequency response of filters 227
3.5 z- transform 233
3.5.1 Definition of the «-transform 234
3.5.2 Existence and convergence of the «-transform 235
3.5.3 Properties of the «-transform 240
3.5.4 «-transform of filters 249
3.6 Discrete Fourier transform 252
3.6.1 Definition of the DFT 252
3.6.2 Properties of the DFT 255
3.6.3 Frequency response of filters 259
3.7 Multirate sequences and systems 264
3.7.1 Downsampling 265
3.7.2 Upsampling 268
3.7.3 Combinations of downsampling and upsampling 270
3.7.4 Combinations of downsampling, upsampling, and filtering 272
3.7.5 Polyphase representation 278
3.8 Stochastic processes and systems 285
3.8.1 Stochastic processes 285
Contents
3.8.2 Systems 288
3.8.3 Discrete-time Fourier transform 292
3.8.4 Multirate sequences and systems 294
3.8.5 Minimum mean-squared error estimation 300
3.9 Computational aspects 303
3.9.1 Fast Fourier transforms 303
3.9.2 Convolution 307
3.9.3 Multirate operations 311
3. A Elements of analysis 313
3.A.1 Complex numbers 313
3.A.2 Difference equations 315
3.A.3 Convergence of the convolution sum 316
3.A.4 Dirac delta function 316
3.B Elements of algebra 318
3.B.1 Polynomials 318
3.B.2 Vectors and matrices of polynomials 321
3.B.3 Kronecker product 324
Chapter at a glance 325
Historical remarks 328
Further reading 328
Exercises with solutions 329
Exercises 336
Functions and continuous-time systems 343
4.1 Introduction 344
4.2 Functions 345
4.2.1 Functions on the real line 345
4.2.2 Periodic functions 351
4.3 Systems 351
4.3.1 Continuous-time systems and their properties 352
4.3.2 Differential equations 355
4.3.3 Linear shift-invariant systems 355
4.4 Fourier transform 359
4.4.1 Definition of the Fourier transform 359
4.4.2 Existence and inversion of the Fourier transform 360
4.4.3 Properties of the Fourier transform 365
4.4.4 Frequency response of filters 373
4.4.5 Regularity and spectral decay 374
4.4.6 Laplace transform 379
4.5 Fourier series 380
4.5.1 Definition of the Fourier series 381
4.5.2 Existence and convergence of the Fourier series 383
4.5.3 Properties of the Fourier series 385
4.5.4 Frequency response of filters 394
4.6 Stochastic processes and systems 395
4.6.1 Stochastic processes 395
4.6.2 Systems 397
4.6.3 Fourier transform 399
Chapter at a glance 401
Historical remarks 403
xiv__________ Contents
Further reading 403
Exercises with solutions 404
Exercises 406
5 Sampling and interpolation 411
5.1 Introduction 412
5.2 Finite-dimensional vectors 420
5.2.1 Sampling and interpolation with orthonormal vectors 421
5.2.2 Sampling and interpolation with nonorthogonal vectors 425
5.3 Sequences 429
5.3.1 Sampling and interpolation with orthonormal sequences 430
5.3.2 Sampling and interpolation for bandlimited sequences 437
5.3.3 Sampling and interpolation with nonorthogonal sequences 442
5.4 Functions 447
5.4.1 Sampling and interpolation with orthonormal functions 449
5.4.2 Sampling and interpolation for bandlimited functions 452
5.4.3 Sampling and interpolation with nonorthogonal functions 470
5.5 Periodic functions 477
5.5.1 Sampling and interpolation with orthonormal periodic functions 477
5.5.2 Sampling and interpolation for bandlimited periodic functions 481
5.6 Computational aspects 489
5.6.1 Projection onto convex sets 491
Chapter at a glance 496
Historical remarks 498
Further reading 498
Exercises with solutions 499
Exercises 503
6 Approximation and compression 507
6.1 Introduction 508
6.2 Approximation of functions on finite intervals by polynomials 513
6.2.1 Least-squares approximation 514
6.2.2 Lagrange interpolation: Matching points 517
6.2.3 Taylor series expansion: Matching derivatives 520
6.2.4 Hermite interpolation: Matching points and derivatives 522
6.2.5 Minimax polynomial approximation 523
6.2.6 Filter design 529
6.3 Approximation of functions by splines 537
6.3.1 Splines and spline spaces 538
6.3.2 Bases for uniform spline spaces 541
6.3.3 Strang-Fix condition for polynomial representation 548
6.3.4 Continuous-time operators in spline spaces implemented with discrete-
time processing 554
6.4 Approximation of functions and sequences by series truncation 560
6.4.1 Linear and nonlinear approximations 560
6.4.2 Linear approximation of random vectors and stochastic processes 566
6.4.3 Linear and nonlinear diagonal estimators 571
6.5 Compression 576
6.5.1 Lossless compression 577
6.5.2 Scalar quantization 579
Contents xv
6.5.3 Transform coding 584
6.6 Computational aspects 591
6.6.1 Huffman algorithm for lossless code design 591
6.6.2 Iterative design of quantizers 593
6.6.3 Estimating from quantized samples 594
Chapter at a glance 597
Historical remarks 598
Further reading 599
Exercises with solutions 600
Exercises 606
7 Localization and uncertainty 615
7.1 Introduction 616
7.2 Localization for functions 619
7.2.1 Localization in time 620
7.2.2 Localization in frequency 622
7.2.3 Uncertainty principle for functions 624
7.3 Localization for sequences 627
7.3.1 Localization in time 629
7.3.2 Localization in frequency 630
7.3.3 Uncertainty principle for sequences 633
7.3.4 Uncertainty principle for finite-length sequences 637
7.4 Tiling the time-frequency plane 638
7.4.1 Localization for structured sets of functions 638
7.4.2 Localization for structured sets of sequences 640
7.5 Examples of local Fourier and wavelet bases 645
7.5.1 Local Fourier and wavelet bases for functions 645
7.5.2 Local Fourier and wavelet bases for sequences 651
7.6 Recap and a glimpse forward 656
7.6.1 Tools 657
7.6.2 Adapting tools to real-world problems 658
7.6.3 Music analysis, communications, and compression 659
Chapter at a glance 666
Historical remarks 667
Further reading 667
Exercises with solutions 668
Exercises 671
Image and quote attribution 673
References 675
Index 681
|
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| isbn | 9781107038608 |
| language | English |
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| spelling | Vetterli, Martin 1957- Verfasser (DE-588)172519853 aut Foundations of signal processing Martin Vetterli, Jelena Kovaěvić, Vivek K. Goyal 1. publ. Cambridge Cambridge University Press 2014 XXVII, 715 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Signal processing Signalverarbeitung (DE-588)4054947-1 gnd rswk-swf Signalverarbeitung (DE-588)4054947-1 s DE-604 Kovačević, Jelena Verfasser aut Goyal, Vivek K. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027523302&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vetterli, Martin 1957- Kovačević, Jelena Goyal, Vivek K. Foundations of signal processing Signal processing Signalverarbeitung (DE-588)4054947-1 gnd |
| subject_GND | (DE-588)4054947-1 |
| title | Foundations of signal processing |
| title_auth | Foundations of signal processing |
| title_exact_search | Foundations of signal processing |
| title_full | Foundations of signal processing Martin Vetterli, Jelena Kovaěvić, Vivek K. Goyal |
| title_fullStr | Foundations of signal processing Martin Vetterli, Jelena Kovaěvić, Vivek K. Goyal |
| title_full_unstemmed | Foundations of signal processing Martin Vetterli, Jelena Kovaěvić, Vivek K. Goyal |
| title_short | Foundations of signal processing |
| title_sort | foundations of signal processing |
| topic | Signal processing Signalverarbeitung (DE-588)4054947-1 gnd |
| topic_facet | Signal processing Signalverarbeitung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027523302&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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