Digital Signal Processing Handbook

Digital Signal Processing Handbook......Page 1
Contents......Page 2
Preface......Page 6
Vijay K. Madisetti......Page 8
Douglas B. Williams......Page 9
Section 1: Signals & Systems......Page 10
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 41
Classical Solution......Page 43
Method of Convolution......Page 51
Difference Equations......Page 53
Initial Conditions and Iterative Solution......Page 54
Classical Solution......Page 56
Method of Convolution......Page 61
Introduction......Page 64
Fixed-Point Quantization Errors......Page 65
Floating-Point Quantization Errors......Page 67
Roundoff Noise in FIR Filters......Page 68
Roundoff Noise in Fixed-Point IIR Filters......Page 69
Roundoff Noise in Floating-Point IIR Filters......Page 72
Limit Cycles......Page 74
Overflow Oscillations......Page 76
Coefficient Quantization Error......Page 77
Realization Considerations......Page 80
Section 2: Signal Representation & Quantization......Page 82
Introduction......Page 84
Definition......Page 85
Fundamental Domains and Cosets......Page 87
The Continuous Space-Time Fourier Transform......Page 88
Sampling and Periodizing......Page 90
The Discrete Fourier Transform......Page 92
Combined Spatial and Frequency Sampling......Page 94
Lattice Chains......Page 95
Change of Variables......Page 96
An Extended Example: HDTV-to-SDTV Conversion......Page 99
Conclusions......Page 101
Introduction......Page 106
Fundamentals of A/D and D/A Conversion......Page 107
Nonideal A/D and D/A Converters......Page 108
Digital-to-Analog Converter Architecture......Page 110
Pipelined A/D Converter......Page 111
Cyclic A/D Converter......Page 113
Delta-Sigma Oversampling Converter......Page 114
Delta-Sigma A/D Converter Architecture......Page 115
Introduction......Page 121
Quantizer and Encoder Definitions......Page 122
Distortion Measure......Page 123
Lloyd-Max Quantizers......Page 124
Linde-Buzo-Gray Algorithm......Page 125
Practical Issues......Page 127
Multistage VQ......Page 129
Split VQ......Page 130
Predictive Speech Coding......Page 131
Speaker Identification......Page 132
Summary......Page 134
Section 3: Fast Algorithms & Structures......Page 136
Ch7 Fast Fourier Transforms: Tutorial Review & State of the Art......Page 138
Introduction......Page 139
From Gauss to the Cooley-Tukey FFT......Page 140
Development of the Twiddle Factor FFT......Page 141
FFTs Without Twiddle Factors......Page 142
State of the Art......Page 143
Motivation (or: why dividing is also conquering)......Page 144
The Cooley-Tukey Mapping......Page 146
Radix-2 and Radix-4 Algorithms......Page 148
Split-Radix Algorithm......Page 153
Remarks on FFTs with Twiddle Factors......Page 155
Basic Tools......Page 156
Winograd's Fourier Transform Algorithm (WFTA)nobreakspace {}cite {03x01.cit56}......Page 163
Remarks on FFTs Without Twiddle Factors......Page 165
Multiplicative Complexity......Page 166
Additive Complexity......Page 168
In-Place Computation......Page 169
Particular Cases and Related Transforms......Page 170
DFT Algorithms for Real Data......Page 171
Related Transforms......Page 172
Multidimensional Transforms......Page 173
Row-Column Algorithms......Page 174
Vector-Radix Algorithms......Page 175
Polynomial Transform......Page 176
General Purpose Computers......Page 179
VLSI......Page 180
Conclusion......Page 181
Introduction......Page 188
Overlap-Add......Page 189
Use of the Overlap Methods......Page 190
Block Convolution......Page 191
Block Recursion......Page 193
Short and Medium Length Convolution......Page 194
The Toom-Cook Method......Page 195
Winograd Short Convolution Algorithm......Page 196
The Split-Nesting Algorithm......Page 198
Multirate Methods for Running Convolution......Page 199
Convolution in Subbands......Page 201
Convolution is Two Dimensional......Page 202
Distributed Arithmetic by Table Lookup......Page 203
Number Theoretic Transforms......Page 204
Special Low-Multiply Filter Structures......Page 206
Introduction......Page 209
One-Dimensional DFTs......Page 214
Multidimensional DFTs......Page 215
Nonstandard Models and Problems......Page 216
Strassen Algorithm......Page 219
Divide-and-Conquer......Page 220
Arbitrary Precision Approximation (APA) Algorithms......Page 221
Number Theoretic Transform (NTT) Based Algorithms......Page 222
Overview......Page 223
The Wavelet Transform......Page 224
Wavelet Representations of Integral Operators......Page 225
Heuristic Interpretation of Wavelet Sparsification......Page 226
Section 4: Digital Filtering......Page 228
Introduction......Page 229
Creating the Design Specifications......Page 230
Specs Derived from Analog Filtering......Page 232
Specifying an Error Measure......Page 233
FIR Characteristics......Page 234
IIR Characteristics......Page 236
Realizing the Designed Filter......Page 237
Realizing IIR Filters......Page 238
Quantization: Finite Wordlength Effect......Page 239
Design by Windowing......Page 240
Optimal Square Error Design......Page 247
Equiripple Optimal Chebyshev Filter Design......Page 250
IIR Design Methods......Page 259
Bilinear Transformation Method......Page 260
Classical IIR Filter Types......Page 261
Maximally Flat Real Symmetric FIR Filters......Page 265
The Affine Filter Structure......Page 270
Optimal Design of FIR Filters with Arbitrary Magnitude and Phase......Page 272
Design of Minimum-Phase FIR Filters......Page 284
Delay Variation of Maximally Flat FIR Filters......Page 287
Combining Criteria in FIR Filter Design......Page 291
Allpass (Phase-Only) IIR Filter Design......Page 299
Magnitude and Phase Approximation......Page 300
Model Order Reduction......Page 301
Filter Design: Graphical User Interface (GUI)......Page 302
Band Edges and Ripples......Page 303
Frequency Scaling......Page 304
Filter Implementation......Page 305
Cascade of Second-Order Sections......Page 307
Scaling for Fixed-Point......Page 308
Comments and Summary......Page 312
Section 5: Statistical Signal Processing......Page 319
Ch12 Overview of Statistical Signal Processing (N/A)......Page 323
Introduction......Page 324
Detector Design Strategies......Page 325
Likelihood Ratio Test......Page 326
Signal Classification......Page 328
The Linear Multivariate Gaussian Model......Page 329
Signal Detection: Known Gains......Page 330
Signal Detection: Unknown Gains......Page 331
Spatio-Temporal Signals......Page 332
Detection: Unknown Gains and Unknown Spatial Covariance......Page 333
Classifying Individual Signals......Page 334
Classifying Presence of Multiple Signals......Page 336
Introduction......Page 338
Random Processes......Page 339
Spectra of Deterministic Signals......Page 340
Spectra of Random Processes......Page 342
The Problem of Power Spectrum Estimation......Page 343
Periodogram......Page 344
The Welch Method......Page 346
Blackman-Tukey Method......Page 347
Minimum Variance Spectrum Estimator......Page 348
Multiwindow Spectrum Estimator......Page 349
Parametric Spectrum Estimation......Page 350
Spectrum Estimation Based on Autoregressive Models......Page 351
Spectrum Estimation Based on Moving Average Models......Page 352
Spectrum Estimation Based on Autoregressive Moving Average Models......Page 353
Pisarenko Harmonic Decomposition Method......Page 354
Multiple Signal Classification (MUSIC)......Page 356
Recent Developments......Page 357
Introduction......Page 359
Least-Squares Estimation......Page 360
Properties of Estimators......Page 362
Best Linear Unbiased Estimation......Page 363
Mean-Squared Estimation of Random Parameters......Page 364
The Basic State-Variable Model......Page 366
Prediction......Page 368
Filtering (the Kalman Filter)......Page 369
Smoothing......Page 371
Digital Wiener Filtering......Page 372
Linear Prediction in DSP, and Kalman Filtering......Page 373
Extended Kalman Filter......Page 374
Introduction......Page 379
Gaussianity, Linearity, and Stationarity Tests......Page 381
Gaussianity Tests......Page 382
Linearity Tests......Page 384
Order Selection......Page 385
Model Validation......Page 386
Confidence Intervals......Page 387
Middleton Class A Noise......Page 388
Stable Noise Distribution......Page 389
Concluding Remarks......Page 390
Introduction......Page 392
Definitions, Properties, Representations......Page 393
Estimation, Time-Frequency Links, Testing......Page 400
Estimating Cyclic Statistics......Page 401
Links with Time-Frequency Representations......Page 402
Testing for Cyclostationarity......Page 403
CS Signals and CS-Inducing Operations......Page 404
Amplitude Modulation......Page 405
Time Index Modulation......Page 406
Fractional Sampling and Multivariate/Multirate Processing......Page 407
Periodically Varying Systems......Page 408
Application Areas......Page 410
CS Signal Extraction......Page 413
Identification and Modeling......Page 415
Concluding Remarks......Page 420
Section 6: Adaptive Filtering......Page 424
What is an Adaptive Filter?......Page 426
Filter Structures......Page 427
The Task of an Adaptive Filter......Page 430
System Identification......Page 431
Inverse Modeling......Page 433
Linear Prediction......Page 435
Feedforward Control......Page 436
The Mean-Squared Error Cost Function......Page 437
The Wiener Solution......Page 438
The LMS Algorithm......Page 439
Other Stochastic Gradient Algorithms......Page 440
System Identification Example......Page 441
Conclusions......Page 443
Introduction......Page 445
Characterizing the Performance of Adaptive Filters......Page 446
Statistical Models for the Input Signal......Page 447
The Independence Assumptions......Page 449
Useful Definitions......Page 450
Mean Analysis......Page 451
Mean-Square Analysis......Page 455
Basic Criteria for Performance......Page 457
Identifying Stationary Systems......Page 459
Tracking Time-Varying Systems......Page 460
Normalized Step Sizes......Page 461
Other Time-Varying Step Size Methods......Page 462
Analysis of Other Adaptive Filters......Page 463
Conclusions......Page 464
Motivation and Example......Page 466
Adaptive Filter Structure......Page 467
Performance and Robustness Issues......Page 468
Robust Adaptive Filtering......Page 469
Energy Bounds and Passivity Relations......Page 472
Min-Max Optimality of Adaptive Gradient Algorithms......Page 473
Comparison of LMS and RLS Algorithms......Page 474
Time-Domain Analysis......Page 475
l2-Stability and the Small Gain Condition......Page 476
Energy Propagation in the Feedback Cascade......Page 478
A Deterministic Convergence Analysis......Page 479
Filtered-Error Gradient Algorithms......Page 480
References and Concluding Remarks......Page 483
Ch21 Recursive Least-Squares Adaptive Filters......Page 486
Array Algorithms......Page 488
Elementary Hyperbolic Rotations......Page 489
Square-Root-Free and Householder Transformations......Page 490
A Numerical Example......Page 491
The Least-Squares Problem......Page 492
Statistical Interpretation......Page 493
The Regularized Least-Squares Problem......Page 494
Statistical Interpretation......Page 495
The Recursive Least-Squares Problem......Page 496
Reducing to the Regularized Form......Page 497
Time Updates......Page 498
Estimation Errors and the Conversion Factor......Page 499
RLS Algorithms in Array Forms......Page 500
The Inverse QR Algorithm......Page 501
The QR Algorithm......Page 504
The Prewindowed Case......Page 506
A Fast Array Algorithm......Page 507
The Fast Transversal Filter......Page 509
Order-Recursive Filters......Page 510
Joint Process Estimation......Page 511
The Backward Prediction Error Vectors......Page 513
The Forward Prediction Error Vectors......Page 515
A Nonunity Forgetting Factor......Page 517
The QRD Least-Squares Lattice Filter......Page 519
The Filtering or Joint Process Array......Page 521
Concluding Remarks......Page 522
Ch22 Transform Domain Adaptive Filtering......Page 525
LMS Adaptive Filter Theory......Page 526
Orthogonalization and Power Normalization......Page 529
Convergence of the Transform Domain Adaptive Filter......Page 531
Discussion and Examples......Page 533
Quasi-Newton Adaptive Algorithms......Page 534
A Fast Quasi-Newton Algorithm......Page 536
The 2-D Transform Domain Adaptive Filter......Page 537
Block-Based Adaptive Filters......Page 539
Comparison of the Constrained and Unconstrained Frequency Domain Block-LMS Adaptive Algorithms......Page 541
Examples and Discussion......Page 544
Introduction......Page 546
The System Identification Framework for Adaptive IIR Filtering......Page 547
Some Preliminaries......Page 549
The LMS and LS Equation Error Algorithms......Page 550
Instrumental Variable Algorithms......Page 552
Equation Error Algorithms with Unit Norm Constraints......Page 553
Gradient-Descent Algorithms......Page 555
Output Error Algorithms Based on Stability Theory......Page 558
The Steiglitz-McBride Family of Algorithms......Page 560
Alternate Parametrizations......Page 563
Conclusions......Page 564
Introduction......Page 566
Channel Equalization in QAM Data Communication Systems......Page 567
Decision-Directed Adaptive Channel Equalizer......Page 569
Basic Facts on Blind Adaptive Equalization......Page 570
Adaptive Algorithms and Notations......Page 571
Mean Cost Functions and Associated Algorithms......Page 572
BGR Extensions of Sato Algorithm......Page 573
Stop-and-Go Algorithms......Page 574
Shalvi and Weinstein Algorithms......Page 575
Summary......Page 576
A Common Analysis Approach......Page 577
Initialization Issues......Page 578
Linearly Constrained Equalizer With Convex Cost......Page 579
Fractionally Spaced Blind Equalizers......Page 580
Concluding Remarks......Page 582
Contents......Page 0
Section 7: Inverse Problems & Signal Reconstruction......Page 585
Introduction......Page 589
Formulation of the Signal Recovery Problem......Page 590
Prolate Spheroidal Wavefunctions......Page 592
Wiener Filtering......Page 594
The Pseudoinverse Solution......Page 595
Regularization Techniques......Page 597
The POCS Framework......Page 598
Row-Based Methods......Page 600
Block-Based Methods......Page 602
Image Restoration Using POCS......Page 603
The Reconstruction Problem......Page 610
Filtered Backprojection (FBP)......Page 611
The Linogram Method......Page 612
Series Expansion Methods......Page 614
Algebraic Reconstruction Techniques (ART)......Page 615
Expectation Maximization (EM)......Page 616
Comparison of the Performance of Algorithms......Page 617
Introduction......Page 620
Speech Production and Spectrum-Related Parameterization......Page 621
Template-Based Speech Processing......Page 622
Robust Speech Processing......Page 623
Affine Transform......Page 626
Deterministic Convolutional Channel as a Linear Transform......Page 627
Additive Noise as a Linear Transform......Page 629
Affine Transform of Cepstral Coefficients......Page 631
Parameters of Affine Transform......Page 633
Correspondence of Cepstral Vectors......Page 635
Background......Page 638
Inverse Problems in DSP......Page 639
Analogies with Statistical Mechanics......Page 640
Combinatorial Optimization......Page 641
Gibbs' Distribution......Page 642
The Simulated Annealing Procedure......Page 643
Introduction......Page 648
The EM Algorithm......Page 649
Example: A Simple MRF......Page 650
Conditional Expectation Calculations......Page 653
Convergence Problem......Page 655
Single Channel Blur Identification and Image Restoration......Page 657
Problem Formulation......Page 663
The E-Step......Page 664
The M-Step......Page 665
Comments on the Choice of Initial Conditions......Page 666
Summary and Conclusion......Page 667
Introduction......Page 673
Wave Propagation......Page 674
Spatial Sampling......Page 675
Narrowband Arrays......Page 676
Look-Direction Constraint......Page 677
Broadband Arrays......Page 678
Narrowband Arrays......Page 681
Row-Action Projection Method......Page 682
Simulation Results......Page 683
Broadband Results......Page 684
Summary......Page 688
Discrete-Time Intersymbol Interference Channel Model......Page 691
Regularization......Page 693
Discrete-Time Adaptive Filtering......Page 695
Adaptive Algorithm Recapitulation......Page 696
Numerical Results......Page 697
Conclusion......Page 699
Introduction: Dereverberation Using Microphone Arrays......Page 700
Simple Delay-and-Sum Beamformers......Page 702
A Brief Look at Adaptive Arrays......Page 704
Constrained Adaptive Beamforming Formulated as an Inverse Problem......Page 707
Matched Filtering......Page 710
Diophantine Inverse Filtering Using the Multiple Input-Output (MINT) Model......Page 713
Results......Page 714
Speaker Identification......Page 716
Summary......Page 720
Introduction......Page 722
Image Formation......Page 726
Side-Looking Airborne Radar (SLAR)......Page 727
Unfocused Synthetic Aperture Radar......Page 728
Focused Synthetic Aperture Radar......Page 729
SAR Image Enhancement......Page 730
Automatic Object Detection and Classification in SAR Imagery......Page 732
Introduction......Page 736
Iterative Recovery Algorithms......Page 737
Basic Iterative Restoration Algorithm......Page 738
Convergence......Page 739
Matrix-Vector Formulation......Page 741
Least-Squares Iteration......Page 742
Basic Iteration......Page 743
Use of Constraints......Page 744
Class of Higher Order Iterative Algorithms......Page 745
Ill-Posed Problems and Regularization Theory......Page 746
Constrained Minimization Regularization Approaches......Page 747
Iteration Adaptive Image Restoration Algorithms......Page 749
Discussion......Page 751
Section 8: Time Frequency & Multirate Signal Processing......Page 755
Filter Banks and Wavelets......Page 759
Deriving Continuous-Time Bases From Discrete-Time Ones......Page 762
Two-Channel Filter Banks and Wavelets......Page 765
Structure of Two-Channel Filter Banks......Page 767
Putting the Pieces Together......Page 770
Ch36 Filter Bank Design......Page 774
Filter Bank Equations......Page 775
The AC Matrix......Page 777
Spectral Factorization......Page 778
Lattice Implementations......Page 779
Time-Domain Design......Page 780
Finite Field Filter Banks......Page 783
Nonlinear Filter Banks......Page 786
Introduction......Page 792
Analysis of Time-Varying Filter Banks......Page 793
Time-Varying Filter Bank Design Techniques......Page 796
Approach I: Intermediate Analysis-Synthesis (IAS)......Page 797
Approach II: Instantaneous Transform Switching (ITS)......Page 800
Conclusion......Page 802
Orthogonal Block Transforms......Page 805
Orthogonal Lapped Transforms......Page 806
Generalized Linear-Phase Lapped Orthogonal Transform (GenLOT)......Page 809
Remarks......Page 810
Section 9: Digital Audio Communications......Page 813
Introduction......Page 816
Pitch......Page 818
Threshold of Hearing......Page 819
Differential Threshold......Page 820
Masked Threshold......Page 821
Summary of Relevant Psychophysical Data......Page 822
Loudness......Page 823
Differential Thresholds......Page 827
Masking......Page 828
Conclusions......Page 838
Introduction......Page 842
Key Technologies in Audio Coding......Page 844
Auditory Masking and Perceptual Coding......Page 845
Frequency Domain Coding......Page 848
Window Switching......Page 849
MPEG-1/Audio Coding......Page 851
The Basics......Page 852
Layers I and II......Page 854
Layer III......Page 856
Frame and Multiplex Structure......Page 858
Subjective Quality......Page 859
MPEG-2/Audio Multichannel Coding......Page 860
Backward-Compatible (BC) MPEG-2/Audio Coding......Page 861
Advanced/MPEG-2/Audio Coding (AAC)......Page 863
Simulcast Transmission......Page 864
MPEG-4/Audio Coding......Page 865
Applications......Page 866
Conclusions......Page 867
Overview......Page 871
Bit Stream Syntax......Page 875
Analysis/Synthesis Filterbank......Page 876
Window Design......Page 877
Transform Equations......Page 878
Spectral Envelope......Page 879
Channel Coupling......Page 882
Rematrixing......Page 884
Parametric Bit Allocation......Page 885
Spreading Function Shape......Page 886
Algorithm Description......Page 887
Quantization and Coding......Page 890
Error Detection......Page 891
Introduction......Page 893
Applications and Test Results......Page 895
Perceptual Coding......Page 896
PAC Structure......Page 898
The EPAC Filterbank and Structure......Page 900
Perceptual Modeling......Page 903
MS vs. LR Switching......Page 905
Noiseless Compression......Page 906
Filterbank and Psychoacoustic Model......Page 907
The Composite Coding Methods......Page 908
Decoder Complexity......Page 909
Conclusions......Page 910
Introduction......Page 912
Concept......Page 913
Actual Converters......Page 915
Film Format......Page 918
Playback System for Digital Sound......Page 919
The SDDS Error Correction Technique......Page 920
Features of the SDDS System......Page 921
Abstract......Page 922
Coder Scheme......Page 924
ATRAC......Page 927
ATRAC2......Page 929
Section 10: Speech Processing......Page 933
Speech Sounds......Page 936
Speech Displays......Page 937
Geometry of the Vocal and Nasal Tracts......Page 938
Acoustical Properties of the Vocal and Nasal Tracts......Page 939
Simplifying Assumptions......Page 940
Wave Propagation in the Vocal Tract......Page 941
The Lossless Case......Page 942
Inclusion of Losses......Page 943
Chain Matrices......Page 944
Nasal Coupling......Page 946
Periodic Excitation......Page 947
Turbulent Excitation......Page 952
Specification of Parameters......Page 954
Synthesis......Page 955
Examples of Applications......Page 957
Speech Coder Attributes......Page 958
The LPC Speech Production Model......Page 960
Model-Based Speech Coders......Page 962
Time Domain Waveform-Following Speech Coders......Page 964
Frequency Domain Waveform-Following Speech Coders......Page 966
Current Standards......Page 967
Current ITU Waveform Signal Coders......Page 968
ITU Linear Prediction Analysis-by-Synthesis Speech Coders......Page 969
Digital Cellular Speech Coding Standards......Page 970
Secure Voice Standards......Page 971
Performance......Page 972
Introduction......Page 976
Text Preprocessing......Page 978
Word Pronunciation......Page 979
Segmental Durations......Page 981
Intonation......Page 982
Speech Synthesis......Page 983
The Future of TTS......Page 985
Introduction......Page 987
Characterization of Speech Recognition Systems......Page 988
``Pattern-Matching'' Approach cite {10x05.Ita75}......Page 989
Speech Recognition by Pattern Matching......Page 990
Pattern Training......Page 991
Pattern Matching......Page 993
Connected Word Recognition......Page 994
Performance of Connected Word Recognizers......Page 995
Sub-Word Speech Units and Acoustic Modeling......Page 996
Speech Recognition System Issues......Page 997
Keyword Spottingnobreakspace {}cite {10x05.WRL90} and Utterance Verificationnobreakspace {}cite {10x05.RLJ95}......Page 998
ASR Applications......Page 999
Introduction......Page 1003
Vocal Personal Identity Characteristics......Page 1004
Basic Elements of a Speaker Recognition System......Page 1005
Extracting Speaker Information from the Speech Signal......Page 1007
Feature Similarity Measurements......Page 1009
Units of Speech for Representing Speakers......Page 1010
Text Dependent (Randomly Prompted Passwords)......Page 1011
Representations That do not Preserve Temporal Characteristics......Page 1012
Optimizing Criteria for Model Construction......Page 1014
Model Training and Updating......Page 1015
Likelihood and Normalized Scores......Page 1016
Cohort or Speaker Background Models......Page 1017
ROC Curves......Page 1018
Outstanding Issues......Page 1019
Software Development Targets......Page 1024
Software Development Paradigms......Page 1025
Assembly Language Basics......Page 1028
Arithmetic......Page 1029
Algorithmic Constructs......Page 1036
Introduction......Page 1039
The User's Environment (OS-Based vs. Workspace-Based)......Page 1040
Display-Oriented Software......Page 1041
Computation vs. Display......Page 1042
Visual (``Point-and-Click'') Interfaces......Page 1043
Parametric Control of Operations......Page 1044
Consistency Maintenance......Page 1045
Real-Time Performance......Page 1046
Support for Speech Input and Output......Page 1047
Summary of Characteristics and Uses......Page 1048
Sources for Finding Out What is Currently Available......Page 1049
Future Trends......Page 1050
Section 11: Image & Video Processing......Page 1051
Introduction......Page 1054
Digital Image Definitions......Page 1055
Characteristics of Image Operations......Page 1056
Convolution......Page 1058
Fourier Transforms......Page 1059
Properties of Fourier Transforms......Page 1060
Statistics......Page 1063
Contour Representations......Page 1068
Brightness Sensitivity......Page 1070
Spatial Frequency Sensitivity......Page 1071
Color Sensitivity......Page 1072
Image Sampling......Page 1074
Sampling Density for Image Processing......Page 1075
Sampling Density for Image Analysis......Page 1077
Photon Noise......Page 1078
On-Chip Electronic Noise......Page 1079
Cameras......Page 1080
Sensitivity......Page 1081
SNR......Page 1082
Shading......Page 1083
Pixel Form......Page 1084
Shutter Speeds (Integration Time)......Page 1085
Displays......Page 1086
Histogram-Based Operations......Page 1087
Mathematics-Based Operations......Page 1089
Convolution-Based Operations......Page 1091
Smoothing Operations......Page 1095
Derivative-Based Operations......Page 1100
Morphology-Based Operations......Page 1105
Shading Correction......Page 1118
Basic Enhancement and Restoration Techniques......Page 1120
Segmentation......Page 1125
Acknowledgments......Page 1137
Introduction......Page 1138
Compressibility of Images......Page 1139
The Ideal Coding System......Page 1140
Coding with Reduced Complexity......Page 1141
Signal Decomposition......Page 1142
Decomposition by Filter Banks......Page 1143
Optimal Transforms/Filter Banks......Page 1146
Decomposition by Differential Coding......Page 1148
Scalar Quantization......Page 1149
Vector Quantization......Page 1151
Efficient Use of Bit-Resources......Page 1152
The JPEG Standard......Page 1154
Improved Coders: State-of-the-Art......Page 1156
Fractal Coding......Page 1158
Mathematical Background......Page 1160
Mean-Gain-Shape Attractor Coding......Page 1161
Color Coding......Page 1163
Introduction......Page 1166
Intra-Frame Observation Model......Page 1167
Multiframe Observation Model......Page 1168
Model Parameter Estimation......Page 1169
Estimation of the Noise Variance......Page 1170
Basic Regularized Restoration Methods......Page 1171
Restoration of Images Recorded by Nonlinear Sensors......Page 1175
Adaptive Restoration for Ringing Reduction......Page 1176
Restoration of Multispectral Images......Page 1177
Restoration of Space-Varying Blurred Images......Page 1178
Multiframe Restoration......Page 1179
Superresolution......Page 1180
Superresolution with Space-Varying Restoration......Page 1181
Conclusion......Page 1182
Introduction......Page 1186
Temporal Interpolation......Page 1187
Vertical Interpolation and Interlaced Scanning......Page 1189
Advanced Algorithms......Page 1190
Pel-Recursive Estimators......Page 1196
Block-Matching Algorithm......Page 1197
Search Strategies......Page 1199
Motion Estimation and Scanning Format Conversion......Page 1201
Hierarchical Motion Estimation......Page 1202
Recursive Search Block-Matching......Page 1203
Introduction......Page 1205
Motion Estimation and Compensation......Page 1206
Transformations......Page 1207
Quantization......Page 1213
Desirable Features......Page 1216
Scalability......Page 1217
Error Resilience......Page 1218
H.261......Page 1219
MPEG-1......Page 1221
MPEG-4......Page 1222
Introduction......Page 1225
MUSE System......Page 1226
HDTV in North America......Page 1227
Hybrid Analog/Digital Systems......Page 1228
FEC......Page 1230
Error Detection and Confinement......Page 1231
Scalable Coding for Error Concealment......Page 1232
Multi-Resolution Transmission......Page 1233
Satellite Transmission......Page 1234
ATM Transmission of Video......Page 1235
ATM Adaptation Layer for Digital Video......Page 1236
Cell Loss Protection......Page 1237
Introduction......Page 1240
Acquisition and Display of Stereoscopic Images......Page 1241
Disparity Estimation......Page 1243
Compression of Stereoscopic Images......Page 1246
Intermediate Viewpoint Interpolation......Page 1247
Image Processing Software......Page 1251
General Image Utilities......Page 1252
Specialized Image Utilities......Page 1254
Programming/Analysis Environments......Page 1255
Images by Form......Page 1256
Introduction......Page 1258
Recent Coding Schemes......Page 1259
Architectural Alternatives......Page 1260
Efficiency Estimation of Alternative VLSI Implementations......Page 1261
Dedicated Architectures......Page 1262
Programmable Architectures......Page 1269
Parallel Data Paths......Page 1270
Coprocessor Concept......Page 1273
Conclusion......Page 1277
Section 12: Sensor Array Processing......Page 1280
Introduction......Page 1283
Representations of Deterministic Signals......Page 1285
Finite-Energy Second-Order Stochastic Processes......Page 1286
Second-Order Complex Stochastic Processes......Page 1288
Complex Representations of Finite-Energy Second-Order Stochastic Processes......Page 1289
Finite-Power Stochastic Processes......Page 1291
Complex Wide-Sense-Stationary Processes......Page 1292
Complex Representations of Real Wide-Sense-Stationary Signals......Page 1293
The Multivariate Complex Gaussian Density Function......Page 1294
Related Distributions......Page 1297
Complex F Distribution......Page 1298
Conclusion......Page 1299
Introduction......Page 1301
Beamforming and Spatial Filtering......Page 1302
Second Order Statistics......Page 1306
Beamformer Classification......Page 1307
Classical Beamforming......Page 1308
General Data Independent Response Design......Page 1309
Multiple Sidelobe Canceller......Page 1312
Use of a Reference Signal......Page 1313
Linearly Constrained Minimum Variance Beamforming......Page 1314
Signal Cancellation in Statistically Optimum Beamforming......Page 1316
Adaptive Algorithms for Beamforming......Page 1317
Interference Cancellation and Partially Adaptive Beamforming......Page 1319
Defining Terms......Page 1320
Introduction......Page 1323
Second-Order Statistics-Based Methods......Page 1324
Signal Subspace Methods......Page 1325
Noise Subspace Methods......Page 1328
Discussion......Page 1330
Higher-Order Statistics-Based Methods......Page 1331
Flowchart Comparison of Subspace-Based Methods......Page 1339
Introduction......Page 1347
Notation......Page 1348
The Standard ESPRIT Algorithm......Page 1349
1-D Unitary ESPRIT in Element Space......Page 1352
1-D Unitary ESPRIT in DFT Beamspace......Page 1354
UCA-ESPRIT for Circular Ring Arrays......Page 1357
FCA-ESPRIT for Filled Circular Arrays......Page 1358
2-D Unitary ESPRIT......Page 1361
2-D Array Geometry......Page 1363
2-D Unitary ESPRIT in Element Space......Page 1366
Automatic Pairing of the 2-D Frequency Estimates......Page 1367
2-D Unitary ESPRIT in DFT Beamspace......Page 1369
Simulation Results......Page 1370
Ch64 Unified Instrumental Variable Approach to Direction Finding in Colored Noise Fields......Page 1375
Introduction......Page 1376
Problem Formulation......Page 1377
The IV-SSF Approach......Page 1379
The Optimal IV-SSF Method......Page 1380
Algorithm Summary......Page 1384
Numerical Examples......Page 1385
Concluding Remarks......Page 1388
Introduction......Page 1393
Single-Source Single-Vector Sensor Model......Page 1395
Multi-Source Multi-Vector Sensor Model......Page 1401
Statistical Model......Page 1402
The Cram'er-Rao Bound......Page 1403
The MSAE......Page 1404
DST Source Analysis......Page 1405
SST Source (DST Model) Analysis......Page 1406
SST Source (SST Model) Analysis......Page 1407
CVAE and SST Source Analysis in the Wave Frame......Page 1409
A Cross-Product-Based DOA Estimator......Page 1411
Results for Multiple Sources, Single-Vector Sensor......Page 1413
Concluding Remarks......Page 1415
Introduction......Page 1420
Short Memory Windows for Time Varying Estimation......Page 1421
Classification of Subspace Methods......Page 1422
Historical Overview of Adaptive, Non-MEP Methods......Page 1423
Controlling Roundoff Error Accumulation and Orthogonality Errors......Page 1424
Spherical Subspace (SS) Updating --- A General Framework for Simplified Updating......Page 1426
Modified Eigen Problems......Page 1430
Gradient-Based Eigen Tracking......Page 1431
Miscellaneous Methods......Page 1432
Formulation of the Problem......Page 1436
AIC and MDL......Page 1438
Decision Theoretic Approaches......Page 1441
The Sphericity Test......Page 1442
Multiple Hypothesis Testing......Page 1443
For More Information......Page 1445
Introduction and Motivation......Page 1446
Multipath Effects......Page 1447
Typical Channels......Page 1448
Signal Model......Page 1449
Block Signal Model......Page 1451
Spatial and Temporal Structure......Page 1452
Single-User ST-ML and ST-MMSE......Page 1454
Multi-User Algorithms......Page 1459
Switched Beam Systems......Page 1461
Channel Reuse Within Cell......Page 1462
References......Page 1463
Introduction......Page 1466
Beamforming......Page 1467
Minimum Output Noise Power Beamforming (MNP)......Page 1469
MMSE Beamformer: Correlated Arrivals......Page 1473
MMSE Beamformer for Mobile Communications......Page 1475
Model of the Array Output......Page 1476
Maximum Likelihood Estimation of ${bf H}$......Page 1477
Experiments......Page 1481
Conclusions......Page 1483
Ch70 Space-Time Adaptive Processing for Airborne Surveillance Radar......Page 1486
Main Receive Aperture and Analog Beamforming......Page 1487
The Processing Needs and Major Issues......Page 1488
Temporal DOF Reduction......Page 1491
Adaptive Filtering with Needed and Sample-Supportable DOF and Embedded CFAR Processing......Page 1493
Space or Space-Range Adaptive Pre-Suppression of Jammers......Page 1495
A STAP Example with a Revisit to Analog Beamforming......Page 1496
Summary......Page 1498
Section 13: Nonlinear & Fractal Signal Processing......Page 1501
Introduction......Page 1504
Modeling and Representation of Chaotic Signals......Page 1505
Use of Chaotic Signals in Communications......Page 1506
Self-Synchronization and Asymptotic Stability......Page 1507
Circuit Implementation and Experiments......Page 1508
Synthesizing Self-Synchronizing Chaotic Systems......Page 1512
Introduction......Page 1518
Eventually Expanding Maps......Page 1519
Estimating Chaotic Signals in Noise......Page 1521
Probabilistic Properties of Chaotic Maps......Page 1522
Statistics of Markov Maps......Page 1524
Power Spectra of Markov Maps......Page 1526
Modeling Eventually Expanding Maps with Markov Maps......Page 1527
Fractal Random Processes......Page 1531
Models and Representations for $1/f$ Processes......Page 1534
Deterministic Fractal Signals......Page 1538
Fractal Point Processes......Page 1539
Multiscale Models......Page 1541
Extended Markov Models......Page 1542
Introduction......Page 1545
Boolean Operators and Threshold Logic......Page 1546
Morphological Set Operators......Page 1547
Morphological Signal Operators and Nonlinear Convolutions......Page 1548
Universality of Morphological Operators......Page 1552
Morphological Operators and Lattice Theory......Page 1555
Slope Transforms......Page 1557
Multiscale Morphological Image Analysis......Page 1560
Binary Multiscale Morphology via Distance Transforms......Page 1562
Differential Equations for Continuous-Scale Morphology......Page 1563
Applications to Image Processing and Vision......Page 1564
Feature Extraction......Page 1565
Shape Representation via Skeleton Transforms......Page 1566
Shape Thinning......Page 1567
Size Distributions......Page 1568
Fractals......Page 1569
Image Segmentation......Page 1570
Conclusions......Page 1571
Introduction......Page 1576
Soliton Systems: The Toda Lattice......Page 1577
The Inverse Scattering Transform......Page 1579
New Electrical Analogs for Soliton Systems......Page 1580
Toda Circuit Model of Hirota and Suzuki......Page 1581
Diode Ladder Circuit Model for Toda Lattice......Page 1582
Circuit Model for Discrete-KdV......Page 1583
Communication with Soliton Signals......Page 1584
Toda Lattice Small Signal Model......Page 1586
Noise Correlation......Page 1587
Inverse Scattering-Based Noise Modeling......Page 1588
Estimation of Soliton Signals......Page 1589
Single Soliton Parameter Estimation: Bounds......Page 1590
Multi-Soliton Parameter Estimation: Bounds......Page 1591
Estimation Algorithms......Page 1592
Estimation Based on Inverse Scattering......Page 1593
Detection of Soliton Signals......Page 1595
Simulations......Page 1596
Introduction......Page 1599
Definitions and Properties of HOS......Page 1600
HOS Computation from Real Data......Page 1603
Linear Processes......Page 1604
Nonparametric Methods......Page 1605
Parametric Methods......Page 1607
Nonlinear Processes......Page 1608
Applications/Software Available......Page 1610
Section 14: DSP Software & Hardware......Page 1614
Introduction......Page 1617
Fixed-Point Devices: TMS320C25 Architecture and Fundamental Features......Page 1618
TMS320C25 Memory Organization and Access......Page 1622
TMS320C25 Multiplier and ALU......Page 1626
TMS320C25 Instruction Set......Page 1629
Subroutines, Interrupts, and Stack on the TMS320C25......Page 1632
Introduction to the TMS320C30 Digital Signal Processor......Page 1633
TMS320C30 Memory Organization and Access......Page 1639
Multiplier and ALU of the TMS320C30......Page 1641
Other Architectural Features of the TMS320C30......Page 1642
TMS320C30 Instruction Set......Page 1643
Other Generations and Devices in the TMS320 Family......Page 1645
Ch78 Rapid Design & Prototyping of DSP Systems......Page 1653
Introduction......Page 1654
Survey of Previous Research......Page 1656
Infrastructure Criteria for the Design Flow......Page 1657
The Executable Requirement......Page 1659
An Executable Requirements Example: MPEG-1 Decoder......Page 1660
The Executable Specification......Page 1661
An Executable Specification Example: MPEG-1 Decoder......Page 1663
Data and Control Flow Modeling......Page 1667
Data and Control Flow Example......Page 1668
Cost Models......Page 1670
Architectural Design Model......Page 1672
Performance Modeling and Architecture Verification......Page 1675
Deterministic Performance Analysis for SCI......Page 1677
DSP Design Case: Single Sensor Multiple Processor (SSMP)......Page 1680
Fully Functional and Interface Modeling andchaptocbreak Hardware Virtual Prototypes......Page 1682
Design Example: I/O Processor for Handling MPEG chaptocbreak Data Stream......Page 1683
Support for Legacy Systems......Page 1684
Conclusions......Page 1687