The digital signal processing fundamentals

DIGITAL SIGNAL PROCESSING FUNDAMENTALS, 2ND ED.......Page 1
Title Page......Page 2
The Electrical Engineering Handbook Series......Page 3
Copyright Page......Page 5
Contents......Page 6
Preface......Page 10
Editor......Page 12
Contributors......Page 14
Part I: Signals and Systems......Page 18
1.1 Introduction......Page 20
1.2.1 Properties of the Continuous-Time Fourier Transform......Page 21
1.2.2 Sampling Models for Continuous- and Discrete-Time Signals......Page 24
1.2.4 Generalized Complex Fourier Transform......Page 25
1.3.1 Exponential Fourier Series......Page 26
1.3.2 Trigonometric Fourier Series......Page 27
1.3.3 Convergence of the Fourier Series......Page 29
1.4 Discrete-Time Fourier Transform......Page 30
1.4.1 Properties of the Discrete-Time Fourier Transform......Page 32
1.4.2 Relationship between the CT and DT Spectra......Page 33
1.5.1 Properties of the DFT......Page 34
1.5.2 Fast Fourier Transform Algorithms......Page 35
1.6.1 Walsh–Hadamard Transform......Page 38
1.7.1 DFT (FFT) Spectral Analysis......Page 39
1.7.2 FIR Digital Filter Design......Page 40
1.7.2.1 Special Case......Page 41
1.7.3.2 Overlap-Add Processing......Page 42
1.7.4 Fourier Domain Adaptive Filtering......Page 43
1.7.5 Adaptive Fault Tolerance via Fourier Domain Adaptive Filtering......Page 46
1.8 Summary......Page 47
References......Page 48
2.1 Differential Equations......Page 50
2.1.1 Role of Auxiliary Conditions in Solution of Differential Equations......Page 51
2.1.2 Classical Solution......Page 52
2.1.2.1 Complementary Solution (the Natural Response)......Page 53
2.1.2.2 Repeated Roots......Page 54
2.1.2.3 Particular Solution (the Forced Response): Method of Undetermined Coefficients......Page 55
2.1.2.4 The Exponential Input e^ζt......Page 57
2.1.2.6 The Complex Exponential Input e^jωt......Page 58
2.1.2.7 The Sinusoidal Input f(t) = cos ω 0 t......Page 59
2.1.3 Method of Convolution......Page 61
2.2 Difference Equations......Page 63
2.2.2 Initial Conditions and Iterative Solution......Page 64
2.2.3 Operational Notation......Page 65
2.2.4.1 Complementary Solution (the Natural Response)......Page 66
2.2.4.3 Particular Solution......Page 68
2.2.4.5 Exponential Input......Page 70
2.2.4.7 A Sinusoidal Input......Page 71
2.2.5 Method of Convolution......Page 72
References......Page 74
3.1 Introduction......Page 76
3.2 Number Representation......Page 77
3.3 Fixed-Point Quantization Errors......Page 78
3.4 Floating-Point Quantization Errors......Page 79
3.5 Roundoff Noise......Page 80
3.5.1 Roundoff Noise in FIR Filters......Page 81
3.5.2 Roundoff Noise in Fixed-Point IIR Filters......Page 82
3.5.3 Roundoff Noise in Floating-Point IIR Filters......Page 85
3.6 Limit Cycles......Page 88
3.7 Overflow Oscillations......Page 89
3.8 Coefficient Quantization Error......Page 90
References......Page 93
Part II: Signal Representation and Quantization......Page 96
4.1 Introduction......Page 98
4.2.1 Definition......Page 99
4.2.3 Reciprocal Lattices......Page 101
4.3.1 The Continuous Space-Time Fourier Transform......Page 102
4.3.3 Sampling and Periodizing......Page 104
4.4.1 The Discrete Fourier Transform......Page 107
4.4.2 Combined Spatial and Frequency Sampling......Page 108
4.5 Lattice Chains......Page 110
4.6 Change of Variables......Page 111
4.7 An Extended Example: HDTV-to-SDTV Conversion......Page 113
4.A.1 Proof of Theorem 4.3......Page 115
4.A.2 Proof of Theorem 4.5......Page 116
4.A.3 Proof of Theorem 4.6......Page 117
Glossary of Symbols and Expressions......Page 118
References......Page 119
5.1 Introduction......Page 120
5.2 Fundamentals of A/D and D/A Conversions......Page 121
5.2.1 Nonideal A/D and D/A Converters......Page 122
5.3 Digital-to-Analog Converter Architecture......Page 124
5.4.1 Flash A/D......Page 125
5.4.3 Pipelined A/D Converter......Page 126
5.4.4 Cyclic A/D Converter......Page 127
5.5 Delta–Sigma Oversampling Converter......Page 128
5.5.1.1 Delta–Sigma Oversampling A/D Converter Principle......Page 129
5.5.1.2 Higher Order Single-Stage Converters......Page 132
References......Page 134
6.1 Introduction......Page 136
6.2.1 Quantizer and Encoder Definitions......Page 137
6.2.3 Optimality Criteria......Page 138
6.3.1 Lloyd–Max Quantizers......Page 139
6.3.2 Linde–Buzo–Gray Algorithm......Page 140
6.4 Practical Issues......Page 142
6.5.1 Multistage VQ......Page 144
6.6.1 Predictive Speech Coding......Page 145
6.6.2 Speaker Identification......Page 146
References......Page 148
Part III: Fast Algorithms and Structures......Page 150
Pierre Duhamel, Martin Vetterli......Page 152
7.1 Introduction......Page 153
7.2.1 From Gauss to the CTFFT......Page 154
7.2.2 Development of the Twiddle Factor FFT......Page 155
7.2.3 FFTs without Twiddle Factors......Page 156
7.3 Motivation (or Why Dividing Is Also Conquering)......Page 157
7.4.1 The Cooley–Tukey Mapping......Page 160
7.4.2 Radix-2 and Radix-4 Algorithms......Page 163
7.4.3 Split-Radix Algorithm......Page 166
7.5.1.1 The Mapping of Good......Page 169
7.5.1.2 DFT Computation as a Convolution......Page 171
7.5.1.3 Computation of the Cyclic Convolution......Page 172
7.5.2 Prime Factor Algorithms......Page 176
7.5.3 Winograd’s Fourier Transform Algorithm......Page 177
7.5.5 Remarks on FFTs without Twiddle Factors......Page 179
7.6.1 Multiplicative Complexity......Page 180
7.6.2 Additive Complexity......Page 182
7.7.2 In-Place Computation......Page 183
7.8.1 DFT Algorithms for Real Data......Page 184
7.8.3 Related Transforms......Page 186
7.9.1 Row–Column Algorithms......Page 188
7.9.2 Vector-Radix Algorithms......Page 189
7.9.3 Nested Algorithms......Page 190
7.9.4 Polynomial Transform......Page 191
7.9.5 Discussion......Page 192
7.10.2 Digital Signal Processors......Page 193
7.11 Conclusion......Page 194
Books......Page 195
1-D FFT Algorithms......Page 196
Related Algorithms......Page 197
Multidimensional Transforms......Page 198
Implementations......Page 199
Software......Page 200
8.1 Introduction......Page 202
8.2.1 Overlap-Add......Page 203
8.2.2 Overlap-Save......Page 204
8.2.3 Use of the Overlap Methods......Page 205
8.3 Block Convolution......Page 206
8.3.1 Block Recursion......Page 207
8.4.1 Toom–Cook Method......Page 209
8.4.2 Cyclic Convolution......Page 210
8.4.3 Winograd Short Convolution Algorithm......Page 211
8.4.5 Split-Nesting Algorithm......Page 213
8.5 Multirate Methods for Running Convolution......Page 214
8.6 Convolution in Subbands......Page 216
8.7.1 Multiplication Is Convolution......Page 217
8.7.3 Distributed Arithmetic by Table Lookup......Page 218
8.8 Fast Convolution by Number Theoretic Transforms......Page 219
8.8.1 Number Theoretic Transforms......Page 220
References......Page 222
9.1 Introduction......Page 226
9.2 One-Dimensional DFTs......Page 231
9.3 Multidimensional DFTs......Page 232
9.6 Nonstandard Models and Problems......Page 233
References......Page 234
10.2.1 Strassen Algorithm......Page 236
10.2.2 Divide-and-Conquer......Page 237
10.2.3 Arbitrary Precision Approximation Algorithms......Page 238
10.2.4 Number Theoretic Transform Based Algorithms......Page 239
10.3.1 Overview......Page 240
10.3.2 Wavelet Transform......Page 241
10.3.3 Wavelet Representations of Integral Operators......Page 243
10.3.4 Heuristic Interpretation of Wavelet Sparsification......Page 244
References......Page 245
Part IV: Digital Filtering......Page 246
11.1 Introduction......Page 248
11.2.1 Creating the Design Specifications......Page 249
11.2.2 Specs Derived from Analog Filtering......Page 251
11.2.3 Specifying an Error Measure......Page 252
11.2.4.1 FIR Characteristics......Page 253
11.2.4.2 IIR Characteristics......Page 254
11.2.5 Designing the Filter......Page 255
11.2.6 Realizing the Designed Filter......Page 256
11.2.6.2 Realizing IIR Filters......Page 257
11.3 Classical Filter Design Methods......Page 258
11.3.1 FIR Design Methods......Page 259
11.3.1.1.1 Steps in Window Filter Design......Page 260
11.3.1.1.2 Window Selection......Page 261
11.3.1.2 Optimal Square Error Design......Page 266
11.3.1.2.1 Discrete Squares Error......Page 267
11.3.1.2.2 Transition Regions......Page 268
11.3.1.3 Equiripple Optimal Chebyshev Filter Design......Page 269
11.3.1.3.3 Alternation Theorem......Page 270
11.3.1.3.4 Remez Algorithm......Page 273
11.3.1.3.5 Design Rules for Lowpass Filters......Page 274
11.3.1.3.7 Summary of Optimal Chebyshev Linear Phase FIR Filter Design......Page 276
11.3.1.3.7.2 Remarks......Page 277
11.3.2.1 Bilinear Transformation Method......Page 278
11.3.2.2.1 Butterworth......Page 279
11.3.2.2.2 Chebyshev: Types I and II......Page 281
11.3.2.2.4 Remarks......Page 282
11.3.2.3 Comments and Generalizations......Page 283
11.4.1.1 Maximally Flat Real Symmetric FIR Filters......Page 285
11.4.1.2 Affine Filter Structure......Page 287
11.4.1.2.1 Prefilters......Page 288
11.4.1.3 Nonsymmetric or Nonlinear Phase FIR Filter Design......Page 289
11.4.1.4.1 Problem Formulation......Page 290
11.4.1.4.2 Design Algorithm......Page 291
11.4.1.4.3 Descent Steps......Page 294
11.4.1.4.4 Descent via the Simplex Method......Page 297
11.4.1.4.5.1 Low Delay Filters with Nearly Linear Phase......Page 298
11.4.1.4.5.3 Seismic Migration Filters......Page 299
11.4.1.6 Delay Variation of Maximally Flat FIR Filters......Page 302
11.4.1.6.1 Problem Formulation......Page 305
11.4.1.6.2 Design Examples......Page 306
11.4.1.6.3 Continuously Tuning ω 0 and G(0)......Page 308
11.4.1.7.1 Savitzky–Golay Filters......Page 309
11.4.1.7.2 Polynomial Smoothing......Page 310
11.4.1.7.3 Moment Preserving Maximal Noise Reduction......Page 311
11.4.1.7.5 Flat Passband, Chebyshev Stopband......Page 312
11.4.1.7.6 Bandpass Filters......Page 313
11.4.1.7.8 Problem Formulation......Page 314
11.4.1.7.9 Design Examples......Page 315
11.4.1.7.10 Quadratic Programming Approach......Page 316
11.4.2.2 Allpass (Phase-Only) IIR Filter Design......Page 317
11.4.2.3 Magnitude and Phase Approximation......Page 318
11.5 Software Tools......Page 319
11.5.1 Filter Design: Graphical User Interface......Page 320
11.5.1.2 Graphical Manipulation of the Specification Template......Page 322
11.5.1.4 Automatic Order Estimation......Page 323
11.5.2 Filter Implementation......Page 324
11.5.2.2 Scaling for Fixed-Point......Page 329
References......Page 330
Part V: Statistical Signal Processing......Page 338
12.1.1 Random Signals and Sequences......Page 342
12.1.1.1 Moments of Random Processes......Page 345
12.1.2.1 Moments and Cumulants......Page 347
12.1.2.2 Frequency and Transform Domain Characterization......Page 350
12.2 Linear Transformations......Page 355
12.3.1 Statistical Description of Random Vectors......Page 357
12.3.2 Moments......Page 358
12.3.3 Linear Transformation of Random Vectors......Page 359
12.3.4.1 Real Gaussian Density......Page 361
12.3.4.2 Complex Gaussian Density......Page 362
12.4.1.1 Maximum Likelihood Estimation......Page 363
12.4.1.2 Properties of Estimates......Page 365
12.4.1.3 Estimates for Moments of Discrete Random Signals......Page 368
12.4.2 Estimation of Random Variables......Page 369
12.4.3 Linear Mean-Square Estimation......Page 370
12.4.3.1 Example......Page 372
Bibliography......Page 373
13.1 Introduction......Page 376
13.2.2 Detector Design Strategies......Page 377
13.2.3 Likelihood Ratio Test......Page 378
13.3 Signal Classification......Page 380
13.4 Linear Multivariate Gaussian Model......Page 381
13.5 Temporal Signals in Gaussian Noise......Page 382
13.5.1 Signal Detection: Known Gains......Page 383
13.5.3 Signal Detection: Random Gains......Page 384
13.6 Spatiotemporal Signals......Page 385
13.6.2 Detection: Unknown Gains and Unknown Spatial Covariance......Page 386
13.7.1 Classifying Individual Signals......Page 387
13.8 Additional Reading......Page 389
References......Page 390
14.1 Introduction......Page 392
14.2.1 Random Processes......Page 393
14.2.2 Spectra of Deterministic Signals......Page 394
14.2.3 Spectra of Random Processes......Page 396
14.3 The Problem of Power Spectrum Estimation......Page 398
14.4.1 Periodogram......Page 399
14.4.3 Welch Method......Page 401
14.4.4 Blackman–Tukey Method......Page 402
14.4.5 Minimum Variance Spectrum Estimator......Page 403
14.4.6 Multiwindow Spectrum Estimator......Page 405
14.5 Parametric Spectrum Estimation......Page 406
14.5.1 Spectrum Estimation Based on Autoregressive Models......Page 407
14.5.2 Spectrum Estimation Based on Moving Average Models......Page 408
14.5.3 Spectrum Estimation Based on Autoregressive Moving Average Models......Page 409
14.5.4 Pisarenko Harmonic Decomposition Method......Page 410
14.5.5 Multiple Signal Classification......Page 412
14.6 Further Developments......Page 413
References......Page 414
15.1 Introduction......Page 416
15.2 Least-Squares Estimation......Page 417
15.3 Properties of Estimators......Page 419
15.4 Best Linear Unbiased Estimation......Page 420
15.5 Maximum-Likelihood Estimation......Page 421
15.6 Mean-Squared Estimation of Random Parameters......Page 422
15.7 Maximum A Posteriori Estimation of Random Parameters......Page 423
15.8 The Basic State-Variable Model......Page 424
15.9.1 Prediction......Page 425
15.9.2 Filtering (Kalman Filter)......Page 426
15.9.3 Smoothing......Page 428
15.10 Digital Wiener Filtering......Page 429
15.11 Linear Prediction in DSP and Kalman Filtering......Page 431
15.13 Extended Kalman Filter......Page 432
References......Page 435
16.1 Introduction......Page 436
16.2 Gaussianity, Linearity, and Stationarity Tests......Page 438
16.2.1 Gaussianity Tests......Page 439
16.2.2 Linearity Tests......Page 441
16.2.3 Stationarity Tests......Page 442
16.3.2 Model Validation......Page 443
16.4.1 Generalized Gaussian Noise......Page 445
16.4.2 Middleton Class A Noise......Page 446
16.5 Concluding Remarks......Page 447
References......Page 448
17.1 Introduction......Page 450
17.2 Definitions, Properties, Representations......Page 451
17.3 Estimation, Time-Frequency Links, and Testing......Page 458
17.3.1 Estimating Cyclic Statistics......Page 459
17.3.2 Links with Time-Frequency Representations......Page 460
17.3.3 Testing for CS......Page 461
17.4.1 Amplitude Modulation......Page 463
17.4.2 Time Index Modulation......Page 464
17.4.3 Fractional Sampling and Multivariate/Multirate Processing......Page 465
17.4.4 Periodically Varying Systems......Page 467
17.5 Application Areas......Page 468
17.5.1 CS Signal Extraction......Page 471
17.5.2 Identification and Modeling......Page 474
17.6 Concluding Remarks......Page 477
References......Page 478
Part VI: Adaptive Filtering......Page 482
18.1 What Is an Adaptive Filter?......Page 484
18.2 Adaptive Filtering Problem......Page 485
18.3 Filter Structures......Page 486
18.5 Applications of Adaptive Filters......Page 488
18.5.1.1 Channel Identification......Page 489
18.5.1.4 Acoustic Echo Cancellation......Page 490
18.5.2 Inverse Modeling......Page 491
18.5.3 Linear Prediction......Page 492
18.5.4 Feedforward Control......Page 493
18.6.1 General Form of Adaptive FIR Algorithms......Page 494
18.6.3 Wiener Solution......Page 495
18.6.4 The Method of Steepest Descent......Page 496
18.6.5 LMS Algorithm......Page 497
18.6.7 Finite-Precision Effects and Other Implementation Issues......Page 498
18.6.8 System Identification Example......Page 499
References......Page 500
19.1 Introduction......Page 502
19.2 Characterizing the Performance of Adaptive Filters......Page 503
19.3.1 System Identification Model for the Desired Response Signal......Page 504
19.3.2.2 Spherically Invariant Random Processes......Page 505
19.3.4 Useful Definitions......Page 507
19.4.1 Mean Analysis......Page 508
19.4.1.1 An Example......Page 510
19.4.2.1 Evolution of the Coefficient Error Correlation Matrix......Page 511
19.4.2.1.2 Analysis for I.I.D. Input Signals......Page 512
19.4.2.2 Excess MSE, Mean-Square Stability, and Misadjustment......Page 513
19.5.1.2 Speed of Convergence......Page 514
19.5.1.3 Misadjustment......Page 515
19.5.3 Tracking Time-Varying Systems......Page 516
19.6.1 Normalized Step Sizes......Page 517
19.6.1.1 Normalized LMS Adaptive Filter......Page 518
19.6.3 Other Time-Varying Step Size Methods......Page 519
References......Page 520
20.1 Motivation and Example......Page 524
20.2 Adaptive Filter Structure......Page 525
20.3 Performance and Robustness Issues......Page 526
20.5 Robust Adaptive Filtering......Page 527
20.6 Energy Bounds and Passivity Relations......Page 530
20.7 Min–Max Optimality of Adaptive Gradient Algorithms......Page 531
20.8 Comparison of LMS and RLS Algorithms......Page 532
20.9.1 Time-Domain Analysis......Page 533
20.9.2 l 2 –Stability and the Small Gain Condition......Page 535
20.9.4 A Deterministic Convergence Analysis......Page 537
20.10 Filtered-Error Gradient Algorithms......Page 538
References......Page 542
Ali H. Sayed, Thomas Kailath......Page 544
21.1 Array Algorithms......Page 546
21.1.2 Elementary Hyperbolic Rotations......Page 547
21.1.3 Square-Root-Free and Householder Transformations......Page 548
21.1.4 A Numerical Example......Page 549
21.2 Least-Squares Problem......Page 550
21.2.1 Geometric Interpretation......Page 551
21.3 Regularized Least-Squares Problem......Page 552
21.3.1 Geometric Interpretation......Page 553
21.3.2 Statistical Interpretation......Page 554
21.4 Recursive Least-Squares Problem......Page 555
21.4.1 Reducing to the Regularized Form......Page 556
21.5 RLS Algorithm......Page 557
21.5.1 Estimation Errors and the Conversion Factor......Page 558
21.6.2 A Very Useful Lemma......Page 559
21.6.3 Inverse QR Algorithm......Page 560
21.6.4 QR Algorithm......Page 562
21.7 Fast Transversal Algorithms......Page 564
21.7.2 Low-Rank Property......Page 565
21.7.3 Fast Array Algorithm......Page 566
21.8 Order-Recursive Filters......Page 569
21.8.1 Joint Process Estimation......Page 570
21.8.2 Backward Prediction Error Vectors......Page 572
21.8.3 Forward Prediction Error Vectors......Page 574
21.8.4 A Nonunity Forgetting Factor......Page 576
21.8.5 QRD-LSL Filter......Page 578
21.9 Concluding Remarks......Page 581
References......Page 582
W. Kenneth Jenkins, C. Radhakrishnan, Daniel F. Marshall......Page 584
22.1 LMS Adaptive Filter Theory......Page 585
22.2 Orthogonalization and Power Normalization......Page 588
22.3 Convergence of the Transform Domain Adaptive Filter......Page 590
22.4 Discussion and Examples......Page 593
22.5 Quasi-Newton Adaptive Algorithms......Page 594
22.5.1 Fast Quasi-Newton Algorithm......Page 595
22.5.2 Examples......Page 596
22.6 2-D Transform Domain Adaptive Filter......Page 597
22.7 Fault-Tolerant Transform Domain Adaptive Filters......Page 600
References......Page 604
23.1 Introduction......Page 606
23.1.1 System Identification Framework for Adaptive IIR Filtering......Page 607
23.1.3 Some Preliminaries......Page 609
23.2.1 LMS and LS Equation Error Algorithms......Page 610
23.2.2 Instrumental Variable Algorithms......Page 612
23.2.3 Equation Error Algorithms with Unit Norm Constraints......Page 614
23.3 Output Error Approach......Page 615
23.3.1 Gradient-Descent Algorithms......Page 616
23.3.2 Output Error Algorithms Based on Stability Theory......Page 619
23.4.1 Steiglitz–McBride Family of Algorithms......Page 621
23.5 Alternate Parametrizations......Page 624
References......Page 625
24.1 Introduction......Page 628
24.2 Channel Equalization in QAM Data Communication Systems......Page 629
24.3 Decision-Directed Adaptive Channel Equalizer......Page 631
24.4 Basic Facts on Blind Adaptive Equalization......Page 632
24.5 Adaptive Algorithms and Notations......Page 633
24.6 Mean Cost Functions and Associated Algorithms......Page 634
24.6.2 BGR Extensions of Sato Algorithm......Page 635
24.6.3 Constant Modulus or Godard Algorithms......Page 636
24.6.5 Shalvi and Weinstein Algorithms......Page 637
24.6.6 Summary......Page 638
24.7 Initialization and Convergence of Blind Equalizers......Page 639
24.7.2 Local Convergence of Blind Equalizers......Page 640
24.8.1 Linearly Constrained Equalizer with Convex Cost......Page 641
24.8.2 Fractionally Spaced Blind Equalizers......Page 642
24.9 Concluding Remarks......Page 644
References......Page 645
Part VII. Inverse Problems and Signal Reconstruction......Page 648
25.1 Introduction......Page 652
25.2 Formulation of the Signal Recovery Problem......Page 653
25.2.1 Prolate Spheroidal Wavefunctions......Page 655
25.3.1 Wiener Filtering......Page 657
25.3.2 Pseudoinverse Solution......Page 659
25.3.3 Regularization Techniques......Page 661
25.4 Signal Recovery using Projection onto Convex Sets......Page 662
25.4.1 POCS Framework......Page 663
25.5 Row-Based Methods......Page 664
25.6 Block-Based Methods......Page 666
25.7 Image Restoration Using POCS......Page 667
References......Page 672
26.2 Reconstruction Problem......Page 674
26.4 Filtered Backprojection......Page 675
26.5 Linogram Method......Page 676
26.6 Series Expansion Methods......Page 678
26.7 Algebraic Reconstruction Techniques......Page 679
26.8 Expectation Maximization......Page 680
26.9 Comparison of the Performance of Algorithms......Page 681
References......Page 682
27.1 Introduction......Page 684
27.2 Speech Production and Spectrum-Related Parameterization......Page 685
27.3 Template-Based Speech Processing......Page 687
27.4 Robust Speech Processing......Page 689
27.5 Affine Transform......Page 691
27.6.1 Deterministic Convolutional Channel as a Linear Transform......Page 692
27.6.2 Additive Noise as a Linear Transform......Page 694
27.7 Affine Transform of Cepstral Coefficients......Page 695
27.8 Parameters of Affine Transform......Page 698
27.9 Correspondence of Cepstral Vectors......Page 700
References......Page 701
28.2 Inverse Problems in DSP......Page 704
28.3 Analogies with Statistical Mechanics......Page 705
28.3.1 Combinatorial Optimization......Page 706
28.3.2 Metropolis Criterion......Page 708
28.4 Simulated Annealing Procedure......Page 709
Further Reading......Page 711
References......Page 712
29.1 Introduction......Page 714
29.2 EM Algorithm......Page 715
29.2.2 Example: A Simple MRF......Page 716
29.3.1 Conditional Expectation Calculations......Page 719
29.3.2 Convergence Problem......Page 722
29.4 Applications......Page 723
29.4.1.2 Maximum Likelihood Parameter Identification......Page 724
29.4.1.3 EM Iterations for the ML Estimation of θ......Page 726
29.4.1.3.1 {u, y} as the Complete Data (CD_uy Algorithm)......Page 727
29.4.1.3.2 {u, v} as the Complete Data (CD_uv Algorithm)......Page 728
29.4.1.4 Iterative Wiener Filtering......Page 729
29.4.3 Problem Formulation......Page 730
29.4.4 E-Step......Page 731
29.5 Experimental Results......Page 733
29.6 Summary and Conclusion......Page 736
References......Page 737
30.1 Introduction......Page 740
30.2.1 Wave Propagation......Page 741
30.2.2 Spatial Sampling......Page 742
30.3 Narrowband Arrays......Page 743
30.3.1 Look-Direction Constraint......Page 744
30.4 Broadband Arrays......Page 745
30.5.1 Narrowband Arrays......Page 748
30.5.2 Broadband Arrays......Page 749
30.5.3 Row-Action Projection Method......Page 750
30.6 Simulation Results......Page 751
30.6.2 Broadband Results......Page 752
References......Page 756
31.2 Discrete-Time Intersymbol Interference Channel Model......Page 758
31.3.1 Matrix Formulation of the Equalization Problem......Page 760
31.4 Regularization......Page 761
31.5.1.2 BINLMS......Page 763
31.5.2 Regularization Properties of Adaptive Algorithms......Page 764
31.7 Conclusion......Page 766
References......Page 767
32.1 Introduction: Dereverberation Using Microphone Arrays......Page 768
32.2 Simple Delay-and-Sum Beamformers......Page 771
32.2.1 A Brief Look at Adaptive Arrays......Page 773
32.2.2 Constrained Adaptive Beamforming Formulated as an Inverse Problem......Page 775
32.2.2.1 Row Action Projection......Page 777
32.3 Matched Filtering......Page 778
32.4 Diophantine Inverse Filtering Using the Multiple Input–Output Model......Page 781
32.5 Results......Page 782
32.5.1 Speaker Identification......Page 786
References......Page 787
33.1 Introduction......Page 790
33.2 Image Formation......Page 794
33.2.1 Side-Looking Airborne Radar......Page 795
33.2.2 Unfocused Synthetic Aperture Radar......Page 796
33.2.3 Focused Synthetic Aperture Radar......Page 797
33.3 SAR Image Enhancement......Page 798
33.4 Automatic Object Detection and Classification in SAR Imagery......Page 800
References......Page 803
34.1 Introduction......Page 804
34.2 Iterative Recovery Algorithms......Page 805
34.3.2 Basic Iterative Restoration Algorithm......Page 806
34.3.3 Convergence......Page 807
34.4 Matrix-Vector Formulation......Page 809
34.4.2 Least-Squares Iteration......Page 810
34.5 Matrix-Vector and Discrete Frequency Representations......Page 811
34.6.1 Basic Iteration......Page 812
34.7 Use of Constraints......Page 813
34.8 Class of Higher Order Iterative Algorithms......Page 814
34.9.2 Constrained Minimization Regularization Approaches......Page 815
34.9.2.2 Projection onto Convex Sets Approach......Page 816
34.9.2.5 Robust Functionals......Page 817
34.9.3.1 Spatially Adaptive Algorithm......Page 818
34.9.3.2 Frequency Adaptive Algorithm......Page 819
34.10 Discussion......Page 820
References......Page 821
Part VIII: Time-Frequency and Multirate Signal Processing......Page 824
35.1 Filter Banks and Wavelets......Page 828
35.1.1 Deriving Continuous-Time Bases from Discrete-Time Ones......Page 831
35.1.2 Two-Channel Filter Banks and Wavelets......Page 834
35.1.3 Structure of Two-Channel Filter Banks......Page 836
35.1.3.1 Orthogonality......Page 837
35.1.3.2 Finite Impulse Response and Symmetric Solutions......Page 839
35.1.4 Putting the Pieces Together......Page 840
References......Page 841
Joseph Arrowood, Tami Randolph, Mark J.T. Smith......Page 844
36.1 Filter Bank Equations......Page 845
36.1.1 AC Matrix......Page 847
36.1.2 Spectral Factorization......Page 848
36.1.3 Lattice Implementations......Page 850
36.1.4 Time-Domain Design......Page 851
36.1.4.1 Functionality of the Design Formulation......Page 853
36.2 Finite Field Filter Banks......Page 854
36.3 Nonlinear Filter Banks......Page 856
References......Page 860
37.1 Introduction......Page 862
37.2 Analysis of Time-Varying Filter Banks......Page 863
37.4.1 Approach I: Intermediate Analysis-Synthesis......Page 867
37.4.2 Approach II: Instantaneous Transform Switching......Page 870
37.5 Conclusion......Page 872
References......Page 873
38.2 Orthogonal Block Transforms......Page 876
38.2.1 Orthogonal Lapped Transforms......Page 877
38.3.1 Extended Lapped Transform......Page 880
38.3.2 Generalized Linear-Phase Lapped Orthogonal Transform......Page 881
38.4 Remarks......Page 882
References......Page 883
Index......Page 886
Back Cover......Page 906