Digital Signal Processing Handbook

Madisetti V., Williams D. (eds.)

Table of contents :
Contents……Page 1
Preface……Page 5
VijayK.Madisetti……Page 7
DouglasB.Williams……Page 8
I. Signals and Systems……Page 9
Introduction……Page 12
Fourier Series Representation of Continuous Timechaptocbreak Periodic Signals……Page 13
Exponential Fourier Series……Page 14
The Trigonometric Fourier Series……Page 15
Convergence of the Fourier Series……Page 17
The Classical Fourier Transform for Continuous Time Signals……Page 18
Fourier Spectrum of the Continuous Time Sampling Model……Page 19
Fourier Transform of Periodic Continuous Time Signals……Page 21
The Discrete Time Fourier Transform……Page 22
Properties of the Discrete Time Fourier Transform……Page 24
Relationship between the Continuous and Discrete Time Spectra……Page 25
The Discrete Fourier Transform……Page 26
Properties of the Discrete Fourier Series……Page 27
Fourier Block Processing in Real-Time Filtering Applications……Page 28
Fast Fourier Transform Algorithms……Page 29
Fast Fourier Transform in Spectral Analysis……Page 32
Finite Impulse Response Digital Filter Design……Page 35
Fourier Analysis of Ideal and Practical Digital-to-Analog Conversion……Page 36
Summary……Page 38
Differential Equations……Page 42
Classical Solution……Page 44
Method of Convolution……Page 52
Difference Equations……Page 54
Initial Conditions and Iterative Solution……Page 55
Classical Solution……Page 57
Method of Convolution……Page 62
Introduction……Page 66
Fixed-Point Quantization Errors……Page 67
Floating-Point Quantization Errors……Page 69
Roundoff Noise in FIR Filters……Page 70
Roundoff Noise in Fixed-Point IIR Filters……Page 71
Roundoff Noise in Floating-Point IIR Filters……Page 74
Limit Cycles……Page 76
Overflow Oscillations……Page 78
Coefficient Quantization Error……Page 79
Realization Considerations……Page 82
II. Signal Representation and Quantization……Page 84
Introduction……Page 87
Definition……Page 88
Fundamental Domains and Cosets……Page 90
The Continuous Space-Time Fourier Transform……Page 91
Sampling and Periodizing……Page 93
The Discrete Fourier Transform……Page 95
Combined Spatial and Frequency Sampling……Page 97
Lattice Chains……Page 98
Change of Variables……Page 99
An Extended Example: HDTV-to-SDTV Conversion……Page 102
Conclusions……Page 104
Introduction……Page 110
Fundamentals of A/D and D/A Conversion……Page 111
Nonideal A/D and D/A Converters……Page 112
Digital-to-Analog Converter Architecture……Page 114
Pipelined A/D Converter……Page 115
Cyclic A/D Converter……Page 117
Delta-Sigma Oversampling Converter……Page 118
Delta-Sigma A/D Converter Architecture……Page 119
Introduction……Page 126
Quantizer and Encoder Definitions……Page 127
Distortion Measure……Page 128
Lloyd-Max Quantizers……Page 129
Linde-Buzo-Gray Algorithm……Page 130
Practical Issues……Page 132
Multistage VQ……Page 134
Split VQ……Page 135
Predictive Speech Coding……Page 136
Speaker Identification……Page 137
Summary……Page 139
III. Fast Algorithms and Structures……Page 141
7. Fast Fourier Transforms: A Tutorial Review and a State of the Art……Page 144
Introduction……Page 145
From Gauss to the Cooley-Tukey FFT……Page 146
Development of the Twiddle Factor FFT……Page 147
FFTs Without Twiddle Factors……Page 148
State of the Art……Page 149
Motivation (or: why dividing is also conquering)……Page 150
The Cooley-Tukey Mapping……Page 152
Radix-2 and Radix-4 Algorithms……Page 154
Split-Radix Algorithm……Page 159
Remarks on FFTs with Twiddle Factors……Page 161
Basic Tools……Page 162
Winograd’s Fourier Transform Algorithm (WFTA)nobreakspace {}cite {03×01.cit56}……Page 169
Remarks on FFTs Without Twiddle Factors……Page 171
Multiplicative Complexity……Page 172
Additive Complexity……Page 174
In-Place Computation……Page 175
Particular Cases and Related Transforms……Page 176
DFT Algorithms for Real Data……Page 177
Related Transforms……Page 178
Multidimensional Transforms……Page 179
Row-Column Algorithms……Page 180
Vector-Radix Algorithms……Page 181
Polynomial Transform……Page 182
General Purpose Computers……Page 185
VLSI……Page 186
Conclusion……Page 187
Introduction……Page 195
Overlap-Add……Page 196
Use of the Overlap Methods……Page 197
Block Convolution……Page 198
Block Recursion……Page 200
Short and Medium Length Convolution……Page 201
The Toom-Cook Method……Page 202
Winograd Short Convolution Algorithm……Page 203
The Split-Nesting Algorithm……Page 205
Multirate Methods for Running Convolution……Page 206
Convolution in Subbands……Page 208
Convolution is Two Dimensional……Page 209
Distributed Arithmetic by Table Lookup……Page 210
Number Theoretic Transforms……Page 211
Special Low-Multiply Filter Structures……Page 213
Introduction……Page 217
One-Dimensional DFTs……Page 222
Multidimensional DFTs……Page 223
Nonstandard Models and Problems……Page 224
Strassen Algorithm……Page 228
Divide-and-Conquer……Page 229
Arbitrary Precision Approximation (APA) Algorithms……Page 230
Number Theoretic Transform (NTT) Based Algorithms……Page 231
Overview……Page 232
The Wavelet Transform……Page 233
Wavelet Representations of Integral Operators……Page 234
Heuristic Interpretation of Wavelet Sparsification……Page 235
IV. Digital Filtering……Page 237
Introduction……Page 239
Creating the Design Specifications……Page 240
Specs Derived from Analog Filtering……Page 242
Specifying an Error Measure……Page 243
FIR Characteristics……Page 244
IIR Characteristics……Page 246
Realizing the Designed Filter……Page 247
Realizing IIR Filters……Page 248
Quantization: Finite Wordlength Effect……Page 249
Design by Windowing……Page 250
Optimal Square Error Design……Page 257
Equiripple Optimal Chebyshev Filter Design……Page 260
IIR Design Methods……Page 269
Bilinear Transformation Method……Page 270
Classical IIR Filter Types……Page 271
Maximally Flat Real Symmetric FIR Filters……Page 275
The Affine Filter Structure……Page 280
Optimal Design of FIR Filters with Arbitrary Magnitude and Phase……Page 282
Design of Minimum-Phase FIR Filters……Page 294
Delay Variation of Maximally Flat FIR Filters……Page 297
Combining Criteria in FIR Filter Design……Page 301
Allpass (Phase-Only) IIR Filter Design……Page 309
Magnitude and Phase Approximation……Page 310
Model Order Reduction……Page 311
Filter Design: Graphical User Interface (GUI)……Page 312
Band Edges and Ripples……Page 313
Frequency Scaling……Page 314
Filter Implementation……Page 315
Cascade of Second-Order Sections……Page 317
Scaling for Fixed-Point……Page 318
Comments and Summary……Page 322
V. Statistical Signal Processing……Page 329
Introduction……Page 336
Detector Design Strategies……Page 337
Likelihood Ratio Test……Page 338
Signal Classification……Page 340
The Linear Multivariate Gaussian Model……Page 341
Signal Detection: Known Gains……Page 342
Signal Detection: Unknown Gains……Page 343
Spatio-Temporal Signals……Page 344
Detection: Unknown Gains and Unknown Spatial Covariance……Page 345
Classifying Individual Signals……Page 346
Classifying Presence of Multiple Signals……Page 348
Introduction……Page 351
Random Processes……Page 352
Spectra of Deterministic Signals……Page 353
Spectra of Random Processes……Page 355
The Problem of Power Spectrum Estimation……Page 356
Periodogram……Page 357
The Welch Method……Page 359
Blackman-Tukey Method……Page 360
Minimum Variance Spectrum Estimator……Page 361
Multiwindow Spectrum Estimator……Page 362
Parametric Spectrum Estimation……Page 363
Spectrum Estimation Based on Autoregressive Models……Page 364
Spectrum Estimation Based on Moving Average Models……Page 365
Spectrum Estimation Based on Autoregressive Moving Average Models……Page 366
Pisarenko Harmonic Decomposition Method……Page 367
Multiple Signal Classification (MUSIC)……Page 369
Recent Developments……Page 370
Introduction……Page 373
Least-Squares Estimation……Page 374
Properties of Estimators……Page 376
Best Linear Unbiased Estimation……Page 377
Mean-Squared Estimation of Random Parameters……Page 378
The Basic State-Variable Model……Page 380
Prediction……Page 382
Filtering (the Kalman Filter)……Page 383
Smoothing……Page 385
Digital Wiener Filtering……Page 386
Linear Prediction in DSP, and Kalman Filtering……Page 387
Extended Kalman Filter……Page 388
Introduction……Page 394
Gaussianity, Linearity, and Stationarity Tests……Page 396
Gaussianity Tests……Page 397
Linearity Tests……Page 399
Order Selection……Page 400
Model Validation……Page 401
Confidence Intervals……Page 402
Middleton Class A Noise……Page 403
Stable Noise Distribution……Page 404
Concluding Remarks……Page 405
Introduction……Page 408
Definitions, Properties, Representations……Page 409
Estimation, Time-Frequency Links, Testing……Page 416
Estimating Cyclic Statistics……Page 417
Links with Time-Frequency Representations……Page 418
Testing for Cyclostationarity……Page 419
CS Signals and CS-Inducing Operations……Page 420
Amplitude Modulation……Page 421
Time Index Modulation……Page 422
Fractional Sampling and Multivariate/Multirate Processing……Page 423
Periodically Varying Systems……Page 424
Application Areas……Page 426
CS Signal Extraction……Page 429
Identification and Modeling……Page 431
Concluding Remarks……Page 436
VI. Adaptive Filtering……Page 440
What is an Adaptive Filter?……Page 443
Filter Structures……Page 444
The Task of an Adaptive Filter……Page 447
System Identification……Page 448
Inverse Modeling……Page 450
Linear Prediction……Page 452
Feedforward Control……Page 453
The Mean-Squared Error Cost Function……Page 454
The Wiener Solution……Page 455
The LMS Algorithm……Page 456
Other Stochastic Gradient Algorithms……Page 457
System Identification Example……Page 458
Conclusions……Page 460
Introduction……Page 463
Characterizing the Performance of Adaptive Filters……Page 464
Statistical Models for the Input Signal……Page 465
The Independence Assumptions……Page 467
Useful Definitions……Page 468
Mean Analysis……Page 469
Mean-Square Analysis……Page 473
Basic Criteria for Performance……Page 475
Identifying Stationary Systems……Page 477
Tracking Time-Varying Systems……Page 478
Normalized Step Sizes……Page 479
Other Time-Varying Step Size Methods……Page 480
Analysis of Other Adaptive Filters……Page 481
Conclusions……Page 482
Motivation and Example……Page 485
Adaptive Filter Structure……Page 486
Performance and Robustness Issues……Page 487
Robust Adaptive Filtering……Page 488
Energy Bounds and Passivity Relations……Page 491
Min-Max Optimality of Adaptive Gradient Algorithms……Page 492
Comparison of LMS and RLS Algorithms……Page 493
Time-Domain Analysis……Page 494
l2-Stability and the Small Gain Condition……Page 495
Energy Propagation in the Feedback Cascade……Page 497
A Deterministic Convergence Analysis……Page 498
Filtered-Error Gradient Algorithms……Page 499
References and Concluding Remarks……Page 502
21. Recursive Least-Squares Adaptive Filters……Page 506
Array Algorithms……Page 508
Elementary Hyperbolic Rotations……Page 509
Square-Root-Free and Householder Transformations……Page 510
A Numerical Example……Page 511
The Least-Squares Problem……Page 512
Statistical Interpretation……Page 513
The Regularized Least-Squares Problem……Page 514
Statistical Interpretation……Page 515
The Recursive Least-Squares Problem……Page 516
Reducing to the Regularized Form……Page 517
Time Updates……Page 518
Estimation Errors and the Conversion Factor……Page 519
RLS Algorithms in Array Forms……Page 520
The Inverse QR Algorithm……Page 521
The QR Algorithm……Page 524
The Prewindowed Case……Page 526
A Fast Array Algorithm……Page 527
The Fast Transversal Filter……Page 529
Order-Recursive Filters……Page 530
Joint Process Estimation……Page 531
The Backward Prediction Error Vectors……Page 533
The Forward Prediction Error Vectors……Page 535
A Nonunity Forgetting Factor……Page 537
The QRD Least-Squares Lattice Filter……Page 539
The Filtering or Joint Process Array……Page 541
Concluding Remarks……Page 542
22. Transform Domain Adaptive Filtering……Page 546
LMS Adaptive Filter Theory……Page 547
Orthogonalization and Power Normalization……Page 550
Convergence of the Transform Domain Adaptive Filter……Page 552
Discussion and Examples……Page 554
Quasi-Newton Adaptive Algorithms……Page 555
A Fast Quasi-Newton Algorithm……Page 557
The 2-D Transform Domain Adaptive Filter……Page 558
Block-Based Adaptive Filters……Page 560
Comparison of the Constrained and Unconstrained Frequency Domain Block-LMS Adaptive Algorithms……Page 562
Examples and Discussion……Page 565
Introduction……Page 568
The System Identification Framework for Adaptive IIR Filtering……Page 569
Some Preliminaries……Page 571
The LMS and LS Equation Error Algorithms……Page 572
Instrumental Variable Algorithms……Page 574
Equation Error Algorithms with Unit Norm Constraints……Page 575
Gradient-Descent Algorithms……Page 577
Output Error Algorithms Based on Stability Theory……Page 580
The Steiglitz-McBride Family of Algorithms……Page 582
Alternate Parametrizations……Page 585
Conclusions……Page 586
Introduction……Page 589
Channel Equalization in QAM Data Communication Systems……Page 590
Decision-Directed Adaptive Channel Equalizer……Page 592
Basic Facts on Blind Adaptive Equalization……Page 593
Adaptive Algorithms and Notations……Page 594
Mean Cost Functions and Associated Algorithms……Page 595
BGR Extensions of Sato Algorithm……Page 596
Stop-and-Go Algorithms……Page 597
Shalvi and Weinstein Algorithms……Page 598
Summary……Page 599
A Common Analysis Approach……Page 600
Initialization Issues……Page 601
Linearly Constrained Equalizer With Convex Cost……Page 602
Fractionally Spaced Blind Equalizers……Page 603
Concluding Remarks……Page 605
Contents……Page 0
VII. Inverse Problems and Signal Reconstruction……Page 608
Introduction……Page 613
Formulation of the Signal Recovery Problem……Page 614
Prolate Spheroidal Wavefunctions……Page 616
Wiener Filtering……Page 618
The Pseudoinverse Solution……Page 619
Regularization Techniques……Page 621
The POCS Framework……Page 622
Row-Based Methods……Page 624
Block-Based Methods……Page 626
Image Restoration Using POCS……Page 627
The Reconstruction Problem……Page 635
Filtered Backprojection (FBP)……Page 636
The Linogram Method……Page 637
Series Expansion Methods……Page 639
Algebraic Reconstruction Techniques (ART)……Page 640
Expectation Maximization (EM)……Page 641
Comparison of the Performance of Algorithms……Page 642
Introduction……Page 646
Speech Production and Spectrum-Related Parameterization……Page 647
Template-Based Speech Processing……Page 648
Robust Speech Processing……Page 649
Affine Transform……Page 652
Deterministic Convolutional Channel as a Linear Transform……Page 653
Additive Noise as a Linear Transform……Page 655
Affine Transform of Cepstral Coefficients……Page 657
Parameters of Affine Transform……Page 659
Correspondence of Cepstral Vectors……Page 661
Background……Page 665
Inverse Problems in DSP……Page 666
Analogies with Statistical Mechanics……Page 667
Combinatorial Optimization……Page 668
Gibbs’ Distribution……Page 669
The Simulated Annealing Procedure……Page 670
Introduction……Page 676
The EM Algorithm……Page 677
Example: A Simple MRF……Page 678
Conditional Expectation Calculations……Page 681
Convergence Problem……Page 683
Single Channel Blur Identification and Image Restoration……Page 685
Problem Formulation……Page 691
The E-Step……Page 692
The M-Step……Page 693
Comments on the Choice of Initial Conditions……Page 694
Summary and Conclusion……Page 695
Introduction……Page 702
Wave Propagation……Page 703
Spatial Sampling……Page 704
Narrowband Arrays……Page 705
Look-Direction Constraint……Page 706
Broadband Arrays……Page 707
Narrowband Arrays……Page 710
Row-Action Projection Method……Page 711
Simulation Results……Page 712
Broadband Results……Page 713
Summary……Page 717
Discrete-Time Intersymbol Interference Channel Model……Page 721
Regularization……Page 723
Discrete-Time Adaptive Filtering……Page 725
Adaptive Algorithm Recapitulation……Page 726
Numerical Results……Page 727
Conclusion……Page 729
Introduction: Dereverberation Using Microphone Arrays……Page 731
Simple Delay-and-Sum Beamformers……Page 733
A Brief Look at Adaptive Arrays……Page 735
Constrained Adaptive Beamforming Formulated as an Inverse Problem……Page 738
Matched Filtering……Page 741
Diophantine Inverse Filtering Using the Multiple Input-Output (MINT) Model……Page 744
Results……Page 745
Speaker Identification……Page 747
Summary……Page 751
Introduction……Page 754
Image Formation……Page 758
Side-Looking Airborne Radar (SLAR)……Page 759
Unfocused Synthetic Aperture Radar……Page 760
Focused Synthetic Aperture Radar……Page 761
SAR Image Enhancement……Page 762
Automatic Object Detection and Classification in SAR Imagery……Page 764
Introduction……Page 769
Iterative Recovery Algorithms……Page 770
Basic Iterative Restoration Algorithm……Page 771
Convergence……Page 772
Matrix-Vector Formulation……Page 774
Least-Squares Iteration……Page 775
Basic Iteration……Page 776
Use of Constraints……Page 777
Class of Higher Order Iterative Algorithms……Page 778
Ill-Posed Problems and Regularization Theory……Page 779
Constrained Minimization Regularization Approaches……Page 780
Iteration Adaptive Image Restoration Algorithms……Page 782
Discussion……Page 784
VIII. Time Frequency and Multirate Signal Processing……Page 788
Filter Banks and Wavelets……Page 793
Deriving Continuous-Time Bases From Discrete-Time Ones……Page 796
Two-Channel Filter Banks and Wavelets……Page 799
Structure of Two-Channel Filter Banks……Page 801
Putting the Pieces Together……Page 804
36. Filter Bank Design……Page 809
Filter Bank Equations……Page 810
The AC Matrix……Page 812
Spectral Factorization……Page 813
Lattice Implementations……Page 814
Time-Domain Design……Page 815
Finite Field Filter Banks……Page 818
Nonlinear Filter Banks……Page 821
Introduction……Page 828
Analysis of Time-Varying Filter Banks……Page 829
Time-Varying Filter Bank Design Techniques……Page 832
Approach I: Intermediate Analysis-Synthesis (IAS)……Page 833
Approach II: Instantaneous Transform Switching (ITS)……Page 836
Conclusion……Page 838
Orthogonal Block Transforms……Page 842
Orthogonal Lapped Transforms……Page 843
Generalized Linear-Phase Lapped Orthogonal Transform (GenLOT)……Page 846
Remarks……Page 847
IX. Digital Audio Communications……Page 850
Introduction……Page 855
Pitch……Page 857
Threshold of Hearing……Page 858
Differential Threshold……Page 859
Masked Threshold……Page 860
Summary of Relevant Psychophysical Data……Page 861
Loudness……Page 862
Differential Thresholds……Page 866
Masking……Page 867
Conclusions……Page 877
Introduction……Page 882
Key Technologies in Audio Coding……Page 884
Auditory Masking and Perceptual Coding……Page 885
Frequency Domain Coding……Page 888
Window Switching……Page 889
MPEG-1/Audio Coding……Page 891
The Basics……Page 892
Layers I and II……Page 894
Layer III……Page 896
Frame and Multiplex Structure……Page 898
Subjective Quality……Page 899
MPEG-2/Audio Multichannel Coding……Page 900
Backward-Compatible (BC) MPEG-2/Audio Coding……Page 901
Advanced/MPEG-2/Audio Coding (AAC)……Page 903
Simulcast Transmission……Page 904
MPEG-4/Audio Coding……Page 905
Applications……Page 906
Conclusions……Page 907
Overview……Page 912
Bit Stream Syntax……Page 916
Analysis/Synthesis Filterbank……Page 917
Window Design……Page 918
Transform Equations……Page 919
Spectral Envelope……Page 920
Channel Coupling……Page 923
Rematrixing……Page 925
Parametric Bit Allocation……Page 926
Spreading Function Shape……Page 927
Algorithm Description……Page 928
Quantization and Coding……Page 931
Error Detection……Page 932
Introduction……Page 935
Applications and Test Results……Page 937
Perceptual Coding……Page 938
PAC Structure……Page 940
The EPAC Filterbank and Structure……Page 942
Perceptual Modeling……Page 945
MS vs. LR Switching……Page 947
Noiseless Compression……Page 948
Filterbank and Psychoacoustic Model……Page 949
The Composite Coding Methods……Page 950
Decoder Complexity……Page 951
Conclusions……Page 952
Introduction……Page 955
Concept……Page 956
Actual Converters……Page 958
Film Format……Page 961
Playback System for Digital Sound……Page 962
The SDDS Error Correction Technique……Page 963
Features of the SDDS System……Page 964
Abstract……Page 965
Coder Scheme……Page 967
ATRAC……Page 970
ATRAC2……Page 972
X. Speech Processing……Page 976
Speech Sounds……Page 980
Speech Displays……Page 981
Geometry of the Vocal and Nasal Tracts……Page 982
Acoustical Properties of the Vocal and Nasal Tracts……Page 983
Simplifying Assumptions……Page 984
Wave Propagation in the Vocal Tract……Page 985
The Lossless Case……Page 986
Inclusion of Losses……Page 987
Chain Matrices……Page 988
Nasal Coupling……Page 990
Periodic Excitation……Page 991
Turbulent Excitation……Page 996
Specification of Parameters……Page 998
Synthesis……Page 999
Examples of Applications……Page 1002
Speech Coder Attributes……Page 1003
The LPC Speech Production Model……Page 1005
Model-Based Speech Coders……Page 1007
Time Domain Waveform-Following Speech Coders……Page 1009
Frequency Domain Waveform-Following Speech Coders……Page 1011
Current Standards……Page 1012
Current ITU Waveform Signal Coders……Page 1013
ITU Linear Prediction Analysis-by-Synthesis Speech Coders……Page 1014
Digital Cellular Speech Coding Standards……Page 1015
Secure Voice Standards……Page 1016
Performance……Page 1017
Introduction……Page 1022
Text Preprocessing……Page 1024
Word Pronunciation……Page 1025
Segmental Durations……Page 1027
Intonation……Page 1028
Speech Synthesis……Page 1029
The Future of TTS……Page 1031
Introduction……Page 1034
Characterization of Speech Recognition Systems……Page 1035
“Pattern-Matching” Approach cite {10×05.Ita75}……Page 1036
Speech Recognition by Pattern Matching……Page 1037
Pattern Training……Page 1038
Pattern Matching……Page 1040
Connected Word Recognition……Page 1041
Performance of Connected Word Recognizers……Page 1042
Sub-Word Speech Units and Acoustic Modeling……Page 1043
Speech Recognition System Issues……Page 1044
Keyword Spottingnobreakspace {}cite {10×05.WRL90} and Utterance Verificationnobreakspace {}cite {10×05.RLJ95}……Page 1045
ASR Applications……Page 1046
Introduction……Page 1051
Vocal Personal Identity Characteristics……Page 1052
Basic Elements of a Speaker Recognition System……Page 1053
Extracting Speaker Information from the Speech Signal……Page 1055
Feature Similarity Measurements……Page 1057
Units of Speech for Representing Speakers……Page 1058
Text Dependent (Randomly Prompted Passwords)……Page 1059
Representations That do not Preserve Temporal Characteristics……Page 1060
Optimizing Criteria for Model Construction……Page 1062
Model Training and Updating……Page 1063
Likelihood and Normalized Scores……Page 1064
Cohort or Speaker Background Models……Page 1065
ROC Curves……Page 1066
Outstanding Issues……Page 1067
Software Development Targets……Page 1073
Software Development Paradigms……Page 1074
Assembly Language Basics……Page 1077
Arithmetic……Page 1078
Algorithmic Constructs……Page 1085
Introduction……Page 1089
The User’s Environment (OS-Based vs. Workspace-Based)……Page 1090
Display-Oriented Software……Page 1091
Computation vs. Display……Page 1092
Visual (“Point-and-Click”) Interfaces……Page 1093
Parametric Control of Operations……Page 1094
Consistency Maintenance……Page 1095
Real-Time Performance……Page 1096
Support for Speech Input and Output……Page 1097
Summary of Characteristics and Uses……Page 1098
Sources for Finding Out What is Currently Available……Page 1099
Future Trends……Page 1100
XI. Image and Video Processing……Page 1101
Introduction……Page 1105
Digital Image Definitions……Page 1106
Characteristics of Image Operations……Page 1107
Convolution……Page 1109
Fourier Transforms……Page 1110
Properties of Fourier Transforms……Page 1111
Statistics……Page 1114
Contour Representations……Page 1119
Brightness Sensitivity……Page 1121
Spatial Frequency Sensitivity……Page 1122
Color Sensitivity……Page 1123
Image Sampling……Page 1125
Sampling Density for Image Processing……Page 1126
Sampling Density for Image Analysis……Page 1128
Photon Noise……Page 1129
On-Chip Electronic Noise……Page 1130
Cameras……Page 1131
Sensitivity……Page 1132
SNR……Page 1133
Shading……Page 1134
Pixel Form……Page 1135
Shutter Speeds (Integration Time)……Page 1136
Displays……Page 1137
Histogram-Based Operations……Page 1138
Mathematics-Based Operations……Page 1140
Convolution-Based Operations……Page 1142
Smoothing Operations……Page 1146
Derivative-Based Operations……Page 1151
Morphology-Based Operations……Page 1156
Shading Correction……Page 1169
Basic Enhancement and Restoration Techniques……Page 1171
Segmentation……Page 1176
Acknowledgments……Page 1188
Introduction……Page 1190
Compressibility of Images……Page 1191
The Ideal Coding System……Page 1192
Coding with Reduced Complexity……Page 1193
Signal Decomposition……Page 1194
Decomposition by Filter Banks……Page 1195
Optimal Transforms/Filter Banks……Page 1198
Decomposition by Differential Coding……Page 1200
Scalar Quantization……Page 1201
Vector Quantization……Page 1203
Efficient Use of Bit-Resources……Page 1204
The JPEG Standard……Page 1206
Improved Coders: State-of-the-Art……Page 1208
Fractal Coding……Page 1210
Mathematical Background……Page 1212
Mean-Gain-Shape Attractor Coding……Page 1213
Color Coding……Page 1215
Introduction……Page 1219
Intra-Frame Observation Model……Page 1220
Multiframe Observation Model……Page 1221
Model Parameter Estimation……Page 1222
Estimation of the Noise Variance……Page 1223
Basic Regularized Restoration Methods……Page 1224
Restoration of Images Recorded by Nonlinear Sensors……Page 1228
Adaptive Restoration for Ringing Reduction……Page 1229
Restoration of Multispectral Images……Page 1230
Restoration of Space-Varying Blurred Images……Page 1231
Multiframe Restoration……Page 1232
Superresolution……Page 1233
Superresolution with Space-Varying Restoration……Page 1234
Conclusion……Page 1235
Introduction……Page 1240
Temporal Interpolation……Page 1241
Vertical Interpolation and Interlaced Scanning……Page 1243
Advanced Algorithms……Page 1244
Pel-Recursive Estimators……Page 1250
Block-Matching Algorithm……Page 1251
Search Strategies……Page 1253
Motion Estimation and Scanning Format Conversion……Page 1255
Hierarchical Motion Estimation……Page 1256
Recursive Search Block-Matching……Page 1257
Introduction……Page 1260
Motion Estimation and Compensation……Page 1261
Transformations……Page 1262
Quantization……Page 1268
Desirable Features……Page 1271
Scalability……Page 1272
Error Resilience……Page 1273
H.261……Page 1274
MPEG-1……Page 1276
MPEG-4……Page 1277
Introduction……Page 1281
MUSE System……Page 1282
HDTV in North America……Page 1283
Hybrid Analog/Digital Systems……Page 1284
FEC……Page 1286
Error Detection and Confinement……Page 1287
Scalable Coding for Error Concealment……Page 1288
Multi-Resolution Transmission……Page 1289
Satellite Transmission……Page 1290
ATM Transmission of Video……Page 1291
ATM Adaptation Layer for Digital Video……Page 1292
Cell Loss Protection……Page 1293
Introduction……Page 1297
Acquisition and Display of Stereoscopic Images……Page 1298
Disparity Estimation……Page 1300
Compression of Stereoscopic Images……Page 1303
Intermediate Viewpoint Interpolation……Page 1304
Image Processing Software……Page 1309
General Image Utilities……Page 1310
Specialized Image Utilities……Page 1312
Programming/Analysis Environments……Page 1313
Images by Form……Page 1314
Introduction……Page 1317
Recent Coding Schemes……Page 1318
Architectural Alternatives……Page 1319
Efficiency Estimation of Alternative VLSI Implementations……Page 1320
Dedicated Architectures……Page 1321
Programmable Architectures……Page 1328
Parallel Data Paths……Page 1329
Coprocessor Concept……Page 1332
Conclusion……Page 1336
XII. Sensor Array Processing……Page 1339
Introduction……Page 1343
Representations of Deterministic Signals……Page 1345
Finite-Energy Second-Order Stochastic Processes……Page 1346
Second-Order Complex Stochastic Processes……Page 1348
Complex Representations of Finite-Energy Second-Order Stochastic Processes……Page 1349
Finite-Power Stochastic Processes……Page 1351
Complex Wide-Sense-Stationary Processes……Page 1352
Complex Representations of Real Wide-Sense-Stationary Signals……Page 1353
The Multivariate Complex Gaussian Density Function……Page 1354
Related Distributions……Page 1357
Complex F Distribution……Page 1358
Conclusion……Page 1359
Introduction……Page 1362
Beamforming and Spatial Filtering……Page 1363
Second Order Statistics……Page 1367
Beamformer Classification……Page 1368
Classical Beamforming……Page 1369
General Data Independent Response Design……Page 1370
Multiple Sidelobe Canceller……Page 1373
Use of a Reference Signal……Page 1374
Linearly Constrained Minimum Variance Beamforming……Page 1375
Signal Cancellation in Statistically Optimum Beamforming……Page 1377
Adaptive Algorithms for Beamforming……Page 1378
Interference Cancellation and Partially Adaptive Beamforming……Page 1380
Defining Terms……Page 1381
Introduction……Page 1385
Second-Order Statistics-Based Methods……Page 1386
Signal Subspace Methods……Page 1387
Noise Subspace Methods……Page 1390
Discussion……Page 1392
Higher-Order Statistics-Based Methods……Page 1393
Flowchart Comparison of Subspace-Based Methods……Page 1401
Introduction……Page 1410
Notation……Page 1411
The Standard ESPRIT Algorithm……Page 1412
1-D Unitary ESPRIT in Element Space……Page 1415
1-D Unitary ESPRIT in DFT Beamspace……Page 1417
UCA-ESPRIT for Circular Ring Arrays……Page 1420
FCA-ESPRIT for Filled Circular Arrays……Page 1421
2-D Unitary ESPRIT……Page 1424
2-D Array Geometry……Page 1426
2-D Unitary ESPRIT in Element Space……Page 1429
Automatic Pairing of the 2-D Frequency Estimates……Page 1430
2-D Unitary ESPRIT in DFT Beamspace……Page 1432
Simulation Results……Page 1433
64. A Unified Instrumental Variable Approach to Direction Finding in Colored Noise Fields……Page 1439
Introduction……Page 1440
Problem Formulation……Page 1441
The IV-SSF Approach……Page 1443
The Optimal IV-SSF Method……Page 1444
Algorithm Summary……Page 1448
Numerical Examples……Page 1449
Concluding Remarks……Page 1452
Introduction……Page 1458
Single-Source Single-Vector Sensor Model……Page 1460
Multi-Source Multi-Vector Sensor Model……Page 1466
Statistical Model……Page 1467
The Cram’er-Rao Bound……Page 1468
The MSAE……Page 1469
DST Source Analysis……Page 1470
SST Source (DST Model) Analysis……Page 1471
SST Source (SST Model) Analysis……Page 1472
CVAE and SST Source Analysis in the Wave Frame……Page 1474
A Cross-Product-Based DOA Estimator……Page 1476
Results for Multiple Sources, Single-Vector Sensor……Page 1478
Concluding Remarks……Page 1480
Introduction……Page 1486
Short Memory Windows for Time Varying Estimation……Page 1487
Classification of Subspace Methods……Page 1488
Historical Overview of Adaptive, Non-MEP Methods……Page 1489
Controlling Roundoff Error Accumulation and Orthogonality Errors……Page 1490
Spherical Subspace (SS) Updating — A General Framework for Simplified Updating……Page 1492
Modified Eigen Problems……Page 1496
Gradient-Based Eigen Tracking……Page 1497
Miscellaneous Methods……Page 1498
Formulation of the Problem……Page 1503
AIC and MDL……Page 1505
Decision Theoretic Approaches……Page 1508
The Sphericity Test……Page 1509
Multiple Hypothesis Testing……Page 1510
For More Information……Page 1512
Introduction and Motivation……Page 1514
Multipath Effects……Page 1515
Typical Channels……Page 1516
Signal Model……Page 1517
Block Signal Model……Page 1519
Spatial and Temporal Structure……Page 1520
Single-User ST-ML and ST-MMSE……Page 1522
Multi-User Algorithms……Page 1527
Switched Beam Systems……Page 1529
Channel Reuse Within Cell……Page 1530
References……Page 1531
Introduction……Page 1535
Beamforming……Page 1536
Minimum Output Noise Power Beamforming (MNP)……Page 1538
MMSE Beamformer: Correlated Arrivals……Page 1542
MMSE Beamformer for Mobile Communications……Page 1544
Model of the Array Output……Page 1545
Maximum Likelihood Estimation of ${bf H}$……Page 1546
Experiments……Page 1550
Conclusions……Page 1552
70. Space-Time Adaptive Processing for Airborne Surveillance Radar……Page 1556
Main Receive Aperture and Analog Beamforming……Page 1557
The Processing Needs and Major Issues……Page 1558
Temporal DOF Reduction……Page 1561
Adaptive Filtering with Needed and Sample-Supportable DOF and Embedded CFAR Processing……Page 1563
Space or Space-Range Adaptive Pre-Suppression of Jammers……Page 1565
A STAP Example with a Revisit to Analog Beamforming……Page 1566
Summary……Page 1568
XIII. Nonlinear and Fractal Signal Processing……Page 1571
Introduction……Page 1575
Modeling and Representation of Chaotic Signals……Page 1576
Use of Chaotic Signals in Communications……Page 1577
Self-Synchronization and Asymptotic Stability……Page 1578
Circuit Implementation and Experiments……Page 1579
Synthesizing Self-Synchronizing Chaotic Systems……Page 1583
Introduction……Page 1590
Eventually Expanding Maps……Page 1591
Estimating Chaotic Signals in Noise……Page 1593
Probabilistic Properties of Chaotic Maps……Page 1594
Statistics of Markov Maps……Page 1596
Power Spectra of Markov Maps……Page 1598
Modeling Eventually Expanding Maps with Markov Maps……Page 1599
Fractal Random Processes……Page 1604
Models and Representations for $1/f$ Processes……Page 1607
Deterministic Fractal Signals……Page 1611
Fractal Point Processes……Page 1612
Multiscale Models……Page 1614
Extended Markov Models……Page 1615
Introduction……Page 1619
Boolean Operators and Threshold Logic……Page 1620
Morphological Set Operators……Page 1621
Morphological Signal Operators and Nonlinear Convolutions……Page 1622
Universality of Morphological Operators……Page 1626
Morphological Operators and Lattice Theory……Page 1629
Slope Transforms……Page 1631
Multiscale Morphological Image Analysis……Page 1634
Binary Multiscale Morphology via Distance Transforms……Page 1636
Differential Equations for Continuous-Scale Morphology……Page 1637
Applications to Image Processing and Vision……Page 1638
Feature Extraction……Page 1639
Shape Representation via Skeleton Transforms……Page 1640
Shape Thinning……Page 1641
Size Distributions……Page 1642
Fractals……Page 1643
Image Segmentation……Page 1644
Conclusions……Page 1645
Introduction……Page 1651
Soliton Systems: The Toda Lattice……Page 1652
The Inverse Scattering Transform……Page 1654
New Electrical Analogs for Soliton Systems……Page 1655
Toda Circuit Model of Hirota and Suzuki……Page 1656
Diode Ladder Circuit Model for Toda Lattice……Page 1657
Circuit Model for Discrete-KdV……Page 1658
Communication with Soliton Signals……Page 1659
Toda Lattice Small Signal Model……Page 1661
Noise Correlation……Page 1662
Inverse Scattering-Based Noise Modeling……Page 1663
Estimation of Soliton Signals……Page 1664
Single Soliton Parameter Estimation: Bounds……Page 1665
Multi-Soliton Parameter Estimation: Bounds……Page 1666
Estimation Algorithms……Page 1667
Estimation Based on Inverse Scattering……Page 1668
Detection of Soliton Signals……Page 1670
Simulations……Page 1671
Introduction……Page 1675
Definitions and Properties of HOS……Page 1676
HOS Computation from Real Data……Page 1679
Linear Processes……Page 1680
Nonparametric Methods……Page 1681
Parametric Methods……Page 1683
Nonlinear Processes……Page 1684
Applications/Software Available……Page 1686
XIV. DSP Software and Hardware……Page 1690
Introduction……Page 1694
Fixed-Point Devices: TMS320C25 Architecture and Fundamental Features……Page 1695
TMS320C25 Memory Organization and Access……Page 1699
TMS320C25 Multiplier and ALU……Page 1703
TMS320C25 Instruction Set……Page 1706
Subroutines, Interrupts, and Stack on the TMS320C25……Page 1709
Introduction to the TMS320C30 Digital Signal Processor……Page 1710
TMS320C30 Memory Organization and Access……Page 1716
Multiplier and ALU of the TMS320C30……Page 1718
Other Architectural Features of the TMS320C30……Page 1719
TMS320C30 Instruction Set……Page 1720
Other Generations and Devices in the TMS320 Family……Page 1722
78. Rapid Design and Prototyping of DSP Systems……Page 1731
Introduction……Page 1732
Survey of Previous Research……Page 1734
Infrastructure Criteria for the Design Flow……Page 1735
The Executable Requirement……Page 1737
An Executable Requirements Example: MPEG-1 Decoder……Page 1738
The Executable Specification……Page 1739
An Executable Specification Example: MPEG-1 Decoder……Page 1741
Data and Control Flow Modeling……Page 1745
Data and Control Flow Example……Page 1746
Cost Models……Page 1748
Architectural Design Model……Page 1750
Performance Modeling and Architecture Verification……Page 1753
Deterministic Performance Analysis for SCI……Page 1755
DSP Design Case: Single Sensor Multiple Processor (SSMP)……Page 1758
Fully Functional and Interface Modeling andchaptocbreak Hardware Virtual Prototypes……Page 1760
Design Example: I/O Processor for Handling MPEG chaptocbreak Data Stream……Page 1761
Support for Legacy Systems……Page 1762
Conclusions……Page 1765