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| Ïîèñê ïî óêàçàòåëÿì |
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| Dudgeon D.E., Mersereau R.M. — Multidimensional Digital Signal Processing |
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| Ïðåäìåòíûé óêàçàòåëü |
Abel transform 387
Addition, of sequences 12
Aliasing, frequency 39 299
Aliasing, spatial 65 66 72 117 119 124—126 205 207 279
All-pass filter 260—262 278 361
All-pole filter 243 263 266 328 331
All-pole spectral estimation 325—331 333
Alpha-rooting 124—126
Anderson and Jury stability theorem 197
Aperture 297 299
Approximation errors in iterative implementation 227—230
Argument principle 193—196 200
Array pattern 294—300 303 306
Array pattern, example 297—299
Array, linear 297—299
Ascent algorithm 131 132
Asterisk notation 16
Autocorrelation function 202 312 319—321 328
Autocorrelation function, coefficients 332—333
Autocorrelation function, matching property 328 332
Autoregressive 325
Back-projection 373—376
Bandlimited impulse response 49
Bandlimited signals 37 42 48 368
Barrier function 273
Bartlett's procedure 317—318
Baseband 42
Baseband, hexagonal 46
Basis function 127
Beam steering 294
Beamforming 290—315
Beamforming, discrete-time 303—311
Beamforming, filter-and-sum 300—301
Beamforming, frequency-domain 301—303 309—311
Beamforming, interpolation 307—309
Beamforming, narrowband 312—315
Beamforming, time-domain 293—301 304—309
Beamforming, weighted delay-and-sum 293—300
BIBO stability 23 190 227 250 271
Bilinear systems 58
Bit-reversal 79 81
Block convolution 116—118
boundary conditions 165 168—171 230—234
Bounded input-bounded output see “BIBO”
Branches, flowgraph 188
Butterfly, matrix 92
Butterfly, vector-radix 77—78
Butterworth filter 259
Capon's spectrum estimator 321—325
Cascade 20 53 132—134 221—223 256 262—263
cat 2 363—379
Causality 23—24 165 201—202
Cepstral stabilization 276—277
Cepstrum 198—208
Cepstrum, computation of 205—208
Cepstrum, existence 199—201
Chebyshev error 127 130—132 253 258
Chebyshev polynomials 138—139 145 259
Chebyshev recursion, network realization 145
Chinese remainder theorem 103
Circuit elements 234—240
Circular convolution 70—74 115 117 125 126
Circular shift 67—68
Composite matrix 90
Computer-aided tomography 2 363—379
Concatenation 380
Concentric squares raster 370—371
Congruent 91
Constraint frequencies 129
Constraint operator 349
Constraints, signal 230—234
Continuous Fourier transform 38 40 89 90
Continuous signals 5
Continuous systems, implementation 47—50
Contraction mapping 384
Convergence of iterative filter implementation 226—228
Convergence of iterative restoration algorithms 351
Convergence, region of 175—180 187
Convolution 15—16 225 264
Convolution, block 116—118
Convolution, circular 70—74 115 117 125 126
Convolution, continuous 291
Convolution, examples 16—20 52
Convolution, implementation using DFTs (example) 71—74
Convolution, linear 72 115 125 126
Convolution, of separable sequences 19 53
Convolution, sum 15 25 113 144 150 174
Convolution, theorem 33 296 301 306
Convolution/back-projection algorithm 373—376 378
Coprime 186
Correlation see “Autocorrelation cross-correlation”
Correlation matrix 313—315
Coset 92
Critical point set 131
Cross-correlation function 312
DeCarlo — Strintzis stability theorem 191—196 198
Decimation-in-time 77 91 96
Deciniation-in-frequency 96
Decomposition of sequence into shifted impulses 13
Deconvolution, constrained 350—354
Deconvolution, time-varying 352
Descent method 72 130 248
DFT see “Discrete Fourier transform”
Difference equation 162—174 182—186 189 218
Differential correction 258
Dimensionality-reducing transformation 388
Direct form II 220—221
Direct form implementation of IIR filters 219—221
Discrete Fourier series 61—63 88
Discrete Fourier series (example) 63
Discrete Fourier Transform 60—106 310—311 369 381
Discrete Fourier transform, calculation 75—86
Discrete Fourier transform, computation of 1-D DFT using M-D DFT 103—106
Discrete Fourier transform, computational considerations 81—86
Discrete Fourier transform, definition 63—66
Discrete Fourier transform, direct calculation 75
Discrete Fourier transform, disk access considerations 83
Discrete Fourier transform, example 65—66
Discrete Fourier transform, for general periodically sampled signals 87—100
Discrete Fourier transform, frequency sampling interpretation 64—65 89
Discrete Fourier transform, hexagonal 97—100
Discrete Fourier transform, implementation of FIR filter 114—118
Discrete Fourier transform, of real sequence 68—69
Discrete Fourier transform, properties 67—74
Discrete Fourier transform, row-column decomposition 75—76 81—82
Discrete Fourier transform, slice 101—103 381
Discrete Fourier transform, used to compute cepstrum 205—207
Disk access considerations for DFT 83
Distortion 348 376
Duality 69 334—335
Eigenfunction 8 182
Eigenvalue 135—136
Eigenvector 135—137
Energy density spectrum 35
entropy 331 (see also “Maximum entropy”)
Equiripple 130
Error 244—245 252 253 258 265
Error norm 126—134
Error, Chebyshev 253
Error, Lp 253
Error, mean-squared 245
Error, modified 247
Error, stability 255—256 272—273
Error, steering 304
Euler's totient function 104
Exponential sequences 8
Extendibility 338—339
Extrapolation 354—355 360
Extremal point 131
Factorization theorem 225
| Factorization, polynomial 133 183 186
Factorization, spectral 202—205 256
Factorization, transcendental 204
Factorization, triangular 271
Fan beams 376—379
Fan filter 274—275
Fan filter, example 55—56
Fast Fourier Transform 60 90 253 310
Fast Fourier transform, for general periodically sampled signals 90—100
Fast Fourier transform, vector-radix 76—86
Feedback 225
FFT see “Fast Fourier transform”
Filter, all-pass 260—262 278 361
Filter, Butterworth 259
Filter, interpolating 307—309
Filter, separable 72 134—137 263
Filter, symmetric half-plane 269—271
Filter, zero-phase see “Zero-phase”
Filtering in wave number-frequency space 291—293
Finite precision arithmetic 146
Finite support constraint 351—352
Finite-extent sequences 9
FIR filter 112—154 163 226 228
FIR filter, cascade 132—134
FIR filter, convolutional implementation 113—114
FIR filter, design using transformations 137—144
FIR filter, design with linear constraints 127
FIR filter, discrete Fourier transform implementation 114—118
FIR filter, equiripple 130—132
FIR filter, hexagonal 149—154
FIR filter, implementation using transformations 144—149
FIR filter, optimal design methods 126—132
FIR filter, parallel 134—137
FIR filter, small generating kernel 148—149
FIR filter, special implementations 132—149
FIR filter, storage requirements 146—148
FIR filter, window design method 118—126
Fixed point 350
Fletcher — Powell algorithm 249 252 255
flowgraphs 187—189 234—240
Fourier transform 31—35 40 50 290 301 302 306 319—321 360 366
Fourier transform, alternative definition 50
Fourier transform, existence 33
Fourier transform, for continuous signals 36 40 89 90
Fourier transform, for window functions 118—119
Fourier transform, inverse 29 37 50 207
Fourier transform, properties 33—35
Fourier transform, short-time 302 309
Fourier-domain constraint 356—359
Frequency response 26—32 49 113 118 127 130 132—135 139 142—143 148 150 228 257
Frequency response, examples 27—28
Frequency response, inverse 29—31
Frequency response, separable systems 28 54
Frequency-domain design techniques for IIR filters 253—262
Fundamental operations 12
Fundamental period 61—62 87
Fundamental theorem of algebra 186 203
Gain, array 313—315
Gain, spatially varying 13
Good's prime factor algorithm 103—106
Gradient methods 133—134 248—250
Grating lobes 297
Hermitian symmetry 68—69
Hessian matrix 249
Hexagonal baseband 46
Hexagonal discrete Fourier transform 97—100
Hexagonal FIR filter 149—154
Hexagonal sampling 44—47
Hexagonal sampling matrix 44—47 98
Hexagonal window 151
High-resolution spectral estimation 321—325
Horizontal period 10 36 61 64 77
Huang's stability theorem 191
IIR filter 112—113 163
IIR filter design, cascade 262—263
IIR filter design, frequency design, zero-phase 256—259
IIR filter design, frequency transformation 259—262
IIR filter design, frequency-domain 253—262
IIR filter design, gradient methods 248—250
IIR filter design, iterative prefiltering 250—252 266
IIR filter design, linearization method 249—250 253—254
IIR filter design, magnitude-only 255—256
IIR filter design, separable denominator 263—266
IIR filter design, Shanks's method 246—248
IIR filter design, space-domain techniques 244—252
IIR filter implementation 218—244
IIR filter implementation, cascade 221—223
IIR filter implementation, column-by-column 172—173
IIR filter implementation, diagonal-by-diagonal 172—173
IIR filter implementation, direct form 219—221
IIR filter implementation, iterative 224—234
IIR filter implementation, minimal realization 243—244
IIR filter implementation, parallel 223—224
IIR filter implementation, row-by-row 236
IIR filter implementation, storage requirements 220—221
IIR filter, all-pole 243 263 266 328 329 331
IIR filter, quadrant 165 219
IIR filter, state-variable model 241
Image enhancement 124
Impulse 291 295
Impulse response 15 114 127 134 137 143 223 224 291
Impulse response, bandlimited 49
Impulse response, determination from frequency response 29—31
Impulse response, determination from frequency response (examples) 30—31
Impulse response, finite-extent see “FIR filter”
Impulse response, infinite extent see “IIR filter”
Impulse response, spatially varying 14
In-place computation 79—81
Index mapping function 172
Information rearrangement 2
Information reduction 2
Initial value theorem 182 208
Input mask 164 220—221
Interpolation 43 48 307—309 369
Interpolation, filter 307—309
Interpolation, function 43
Inverse Fourier transform 29 37 50 207
Inverse function 323
Inverse operator 349
Inverse problems 348—383
Inverse problems, definition 348
Inverse z-transform 186—187
Irreducible 186
Isopotential 140—142
Iterative implementation for IIR filters 224—234
Iterative prefiltering 250—252 266
Justice and Shanks's stability theorem 197
Lagrange multiplier 322 333
Lattice structures 266—275
Least-squares design of FIR filters 128—132
Levenburg — Marquardt algorithm 250 255
Line impulse 7
Linear array 297—299
Linear convolution see “Convolution”
Linear phase 200 309
Linear prediction 327—328
Linear programming 131 258
Linear systems 14 168
Linear transformation 24 168 182
Linearity, of DFT 67
Linearity, of Fourier transform 33
Linearization method 249—250 253—254
Logarithm, complex 199
Lowpass filter, ideal 30—31 66
Lowpass filter, window design example 120—124
Magnitude-only filter design 255—256
Mapping from wedge to quadrant 24
Mapping function 172
Mapping, linear 24 168 182
Matrix, block Toeplitz 324
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