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| Dudgeon D.E., Mersereau R.M. — Multidimensional Digital Signal Processing |
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| Ïðåäìåòíûé óêàçàòåëü |
Matrix, composite 90
Matrix, correlation 313—315
Matrix, Hessian 249
Matrix, inverse 324
Matrix, periodicity 11 41 48 51 87—88 96
Matrix, sampling 39—51 89 98
Matrix, Toeplitz 270
Matrix, unimodular 90
Maximum entropy spectral estimation 331—338
Maximum likelihood 314
McClellan transformation 137—148 258—259
McClellan transformation, hexagonal 152—153
Migration, seismic wave 359—363
Minimal realizations 243—244
minimax 130
Minimization procedure 244—246 248—250 253—254
Mixed-radix decompositions 81
Modulation 34 69
Multidimensional digital signal processing 2—3
Multidimensional signals 5—12
Multidimensional systems 12—26
Multiplication, scalar, of sequences 12
Newton's method 249—250
Nodes, flowgraph 188
Noise, white 326 328 339
Nonessential singularities 186 197
Nonexpansive operator 384
Nonlinear phase 113
Nonlinearity, memoryless 13
Nonrecursive filter 112
Nonsymmetric half-plane 204—205 278—279
Nonsymmetric half-plane, filter 166—168 170 183 257
Norm 126—134
Normal equations 247
NSHP see “Nonsymmetric half-plane”
Nyquist stability criterion 192
Operations, fundamental 12
Operators, nonlinear 13
Optimization, constrained 322 332—335
Order, of difference equations 163
Ordering relation 172 187 236
Ordering, computation of output samples 171—174
Output mask 164 167 171 220—221 270
Overlap-add 116—117
Overlap-save 117—118
O’Connor's stability theorem 196
Padding with zeroes 67
parallel 21 53 134—137 223—224 257
Parseval's theorem 35 50 69 128 182 245 253
Partial ordering 171
Penalty function 255 273
Period 10
Period, fundamental 61—62 87
Period, horizontal 10 36 61 64 77
Period, vertical 10 36 61 64 77
periodic extension 38 41 63 64 70—71 88
Periodic sequences 9—12
Periodically sampled signals, discrete Fourier transforms for 87—100
Periodicity matrix 11 41 48 51 87—88 96
Periodicity vectors 11
Periodogram 317—321
Periodogram, modified 317—318
Periodogram, smoothed 318—319
Phase 255
Phase convergence of iterative implementation 229
Phase, linear 359
Phase, linear, removal 200
Phase, maximum 201 256 278
Phase, minimum 201—205 207 255—256 267—268 271 276—278 328
Phase, nonlinear 113
Phase, unwrapped 194—196 200 206
Pipeline 223
Plane wave 290—291 294—295 301 304 314 329 338
Polar raster 369
Poles 183—184 201
Polynomial 183
Polynomial, Chebyshev 138—139 145 259
Polynomial, factorization 133 183 186
Polynomial, numerator, effect on stability 196—197
Positive-definite 328
Positivity operator 349 351 352
Power spectrum 313—316 325 327
Power spectrum, inverse 324
Precedence graph 171—172
Prime factor algorithm 103—106
Prime matrix 90
Projection-slice theorem 366—367 381
Projections 363—366
Projections, of discrete signals 379—383
Propagating waves 289—294
Quadrant 165 167 171
Quantization, delay 304—305
Radon kernel 367 379
Reconstruction, convolution/back-projection 373—378
Reconstruction, Fourier-domain algorithms 369—372
Reconstruction, from fan beams 376—379
Reconstruction, from magnitude or phase 356—359
Reconstruction, from projections 363—379
Reconstruction, iterative 376
Reconstruction, of continuous signal from samples 39 42
Rectangular sampling 36—39
Rectangularly periodic 11 61—63 70
Recursion 267—268
Recursion, direction of 165—168
Recursive computability 164—168
Recursive filter 112—113 244
Recursive formula for partial derivatives 246
Recursive formula to compute cepstrum 207—208
Recursive systems 162—174 182—186
Recursive systems, hexagonal 214—215
Recursive systems, stability 189—198
Reflection coefficients 266 268 269
Reflection functions 268 271 275
Region of analyticity see “Region of convergence”
Region of convergence 175—180 187
Reinhardt domain 175
Remainder theorem 103
Remez, second algorithm 131
Residue theorem 187
Resolution limits in CAT 367—368
Restoration, constrained 349—359
Root map 184—186 192 194
Roots 183 192 194 203
Row-column decomposition 96—97
Sample 6
Sampling 36—47
Sampling density 43
Sampling frequency 39
Sampling intervals 36
Sampling matrix 39—51 89 98
Sampling matrix, hexagonal 44 46 47 98
Sampling theorem 39 65 368
Sampling vectors 39
Sampling, comparison of rectangular and hexagonal 44—47
Sampling, example 43
Sampling, periodic 36—47
Sampling, periodic, with arbitrary sampling geometries 39—44 56 57
Sampling, periodic, with rectangular geometry 36—39
Separable denomiator filter 263—266
Separable filter 72 263
Separable filter, multistage 134—137
Separable sequence 8—9
Separable sequence, cepstrum of 199
Separable sequence, z-transform of 180
Separable systems 22
Sequences 6—12 (see also “Signals”)
| Sequences, finite-extent 9
Sequences, periodic 9—12 64
Sequences, separable 8 19 53
Shanks's method for IIR filter design 246—248
Shanks's stability theorem 191
Shaw's stabilization method 277—279
Sheet impulse 7
shift operators 188 234—244
Shift operators, minimizing the number of 238—240
Shift register 236
Shift, linear 13
Shift-free paths 241
Shift-invariant 14—15 169
Shift-varying 169
Short-Time Fourier Transform 302 309
Signal-domain constraint 356—359
Signals 1
Signals, array 311
Signals, bandlimited 37 42 48
Signals, continuous 5
Signals, discrete 5—12
Signals, elemental 290
Signals, mixed 5
Signals, multidimensional 5—12
Signals, space-time 289—347
Singularities 183
Singularities, nonessential 186 197
Sinusoid, complex 8
Slice 366—367
Slice DFT 101—103 381—383
Slowness vector 291 301 304
Small generating kernel 148—149
Space-domain design of IIR filters 244—252
Space-time signals 289—347
sparse array 341
Spectral estimate, inverse 324 331
Spectral estimation 315—338
Spectral estimation, all-pole 325—331
Spectral estimation, autoregressive 325
Spectral estimation, classical 316—321
Spectral estimation, high-resolution 321—325
Spectral estimation, maximum entropy 331—338
Spectral factorization 202—205 256
Spectrum, wavenumber-frequency 290
Spherical wave 314
Stability 23 33 54 113 189—198 250 260 269 271
Stability constraint 255—256
Stability error 255—256 272—273
Stability testing 193—196
Stability theorems 190—193 197—198
Stability theorems, half-plane 277
Stability, BIBO 23 190 227 250 271
Stability, definitions 23
Stability, effect of numerator polynomial 196—197
Stability, mean-square 23 33
Stability, Nyquist 192
Stabilization 218 254 276—279
State variable realizations 240—244
Steepest descent method 130 248
Steering delays 293—294 301 304—305 310 312
Step response 52—53
STORE operator 227 231
Superposition 14 15 113
Support, continuous 268
Support, everywhere 179
Support, finite 176
Support, on a half-plane 179
Support, on a wedge 24 178
Support, quadrant 24 176—177 204
Support, region of 9 23—25 63 115—119 201—202
Support, symmetric half-plane 278
Symmetric half-plane filter 269—271
Symmetric half-plane support 278
Symmetry in hexagonal FIR filters 150 159
System function see “Transfer function”
Systems, active 289
Systems, cascade 20 53 132—134 221—223 256 262 263
Systems, linear 14 168
Systems, linear shift-invariant 15—22 52 182
Systems, multidimensional 12—26
Systems, parallel 21 53 134—137 223—224 257
Systems, passive 289
Systems, recursive 162—174 182—186
Systems, separable 22
Systems, shift-invariant 14—15 169
Systems, stable 23
Systems, vector input-output 25—26
Taylor series 249
Time-varying deconvolution 352
Toeplitz matrix 270
Tomography 2 363—379
Totient function 104
Trace 313
Transcendental factorization 204
Transfer function 174 182—188 199 222 223 234 272
Transformation, dimensionality-reducing 388
Transformation, for FIR filter design 137—144
Transformation, for FIR filter implementation 144—149
Transformation, frequency 259—262
Transformation, function 139 142 152
Transformation, linear 24 168 182
Transformation, McClellan 137—148 152—153 258—259
TRANSPOSE 10 65 83
Transposition 83—86
Transposition, theorem 239—240
Truncation 230—234
Twiddle factors 92 93 95
Unimodular matrix 90
Unit bicircle 175
Unit impulse 7 13
Unit ramp 244
Unit sample 7 244
Unit step 8 16 244
Unit surface 175
Unwrapped phase 194—196 200 206
Upsampler 307—309
Vector filtering 269
Vector input-output systems 25—26
Vector-radix decomposition 97
Vector-radix fast Fourier transform 76—86
Vertical period 10 36 61 64 77
Wave equation, hyperbolic 359 386
Wavelength 339
Wavenumber 290
Wavenumber-frequency response 292—293 296 301 305
Wavenumber-frequency spectrum 290—293 295
Weights, receiver 299—300
Welch's spectrum estimator 318
White noise 326 328 339
Window 118—124 126 151 299—300
Window, design example 120—124
Window, design method 118—126
Window, function 118—119
Window, Gaussian 126
Window, Harming 119
Window, hexagonal 151
Window, Kaiser 120—121
Window, outer product 119 121 124 151
Window, rectangular 119
Window, rotated 119 121 124 151
Wordlength 240
z-transform 174—189 381
z-transform, inverse 186—187 261
z-transform, properties 180—182
Zero-padding 67
Zero-phase 113—114 127 130 137 139 256
zeros 183—184 194 196 197 201
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