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| Goswami J., Chan A. — Fundamentals of Wavelets. Theory, Algorithms, and Applications |
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| Предметный указатель |
 -spline 45
Acoustic signals 221
Adaptive resonance theory 248
Admissibility condition 69
Algorithms, CAD 244
Algorithms, computer programs 184 258 263
Algorithms, decomposition 149
Algorithms, FFT-based 200
Algorithms, filter bank 141
Algorithms, marching 257
Algorithms, pyramid decomposition 210
Algorithms, reconstruction 153
Algorithms, three-dimensional wavelet 255
Algorithms, two-dimensional wavelet 233
Algorithms, wavelet packet 210 212 234
Algorithms, zero-tree 236
Aliasing 143
Ambiguity function 83
Analyzing wavelet 94
Antialiasing condition 174 184
Approximation subspace 148
Arithmetic code 235
ART 248
Autocorrelation 95 135 149
Averaging filter 25
Basis functions 9
Basis functions, biorthogonal 11
Basis functions, dual 11
Basis functions, entire-domain 272
Basis functions, global 272
Basis functions, Haar 13
Basis functions, local 13 272
Basis functions, orthonormal 11
Basis functions, Riesz 13
Basis functions, semiorthogonal 11
Basis functions, stable 15
Basis functions, subdomain 272
Battle — Lemarie wavelet 123
Bernstein polynomial 295
Best basis selection 220
Binary phase-shift key 252
Binary scales 187
Binomial theorem 136
Biorthogonal basis 11
Biorthogonal decomposition 93
Biorthogonal filter bank 174
Biorthogonal wavelets 95 108 129
Biorthogonal wavelets, Cohen, Daubechies, and Feaveau 130
Biorthogonality condition 93 179
Bit plane coding 235
Boundary condition 269
Boundary value problems 267
Boundary wavelets 281
Bounded interval 280
BPSK 252 5
BVP 267
CAD algorithm 244
Cardinal -splines 112
Causal filter 176
Causality 176
Centered integral wavelet transform 196
Change of bases 21 154 157 160
Chirp signal 68 204
Chui — Wang wavelet 112
CIWT 196
Cluster detection 244
Coding, arithmetic 235
Coding, bit plane 235
Coding, entropy 238
Coding, EZW 238
Coding, Huffman 235
Coding, image 235
Coding, lossy 235
Coding, predictive 235
Coding, runtength 235
Coding, wavelet tree 236
Cohen, Daubechies, and Feaveau wavelet 130
Coiflets 137
Comb function 33
Comer smoothing functions 120
Computer programs, 1-D algorithm 184
Computer programs, 2-D algorithm 258
Computer programs, B-spline 106
Computer programs, iterative method 139
Computer programs, short-time Fourier transform 85
Computer programs, wavelet 138
Computer programs, wavelet packet 263
Computer programs, Wigner — Ville distribution 86
Condition number 291
Continuous wavelet transform 67
Conventional bases 273
Conventional MoM 268
Convolution 24 39 147
Correlation function 81
Crack detection 202
Critical sampling 150
Cubic spline 159 162
Cut-off frequency 205
CWT 67 150
Danielson and Lanczos 55
Daubechies 211
Daubechies wavelet 125
Daubechies’ orthogonal filters 176
DCT 245
Decimation 142 147
Decomposition relation 97 151
Design origin 183
Determinant 19
DFT 55
Differential equations 294
Differential operator 272
Differentiating filter 25
Digital Signal Processing 210
Dilation (refinement) equation 91
Dilation parameters 69
Direct sum 91
Direct-sum decomposition 91
Direction decomposition 210
Dirichlet kernel 55
Discontinuity problem 276
Discrete Fourier basis 50
Discrete Fourier Transform 54
Discrete Gabor representation 65
Discrete short-time Fourier transform 64
Discrete wavelet transform 67 72
Discrete-time Fourier transform 52
Dispersive nature 205
Doppler 83
Doppler frequencies 165
DTFT 52
Dual basis 11
Dual scaling function 157
Dual spline 154
Dual wavelet 93
Duality 93
Duality principle 155
DWT 67 182
Dyadic points 156 187
Edge effect 281
Eigenmatrix 19
Eigensystem 19
Eigenvalue 19
Eigenvalue method 134
Eigenvectors 20
Electromagnetic scattering 268
Elliptic PDEs 295
Embedded zerotree wavelet 238
Entire-domain basis 272
Entropy coder 238
Error considerations 282
| Euclidean vector space 7
Euler Frobenius Laurent polynomial 108 114 157
Evolution problems 295
EZW 238
False positives 249
Fast integral transform 187
Faulty bearing 221
Feature extraction, spectral 227
Feature extraction, wavelet packets 227
Feature extraction, wavelets 226
FEM 294
FFT 55 226
FFT-based algorithm 200
Filter bank 141 180
Filter bank algorithms 141
Filters, averaging 25
Filters, biorthogonal 174
Filters, causal 176
Filters, differentiating 25
Filters, filter bank 141 180
Filters, FIR 114 156 172
Filters, half-band 172
Filters, HBF 172
Filters, highpass 25
Filters, IIR 114 172
Filters, lowpass 25 102
Filters, noncausal symmetric 172
Filters, perfect reconstruction 177
Filters, PR condition 167 184
Filters, PR filter bank 166 182
Filters, PR requirements 177
Filters, QMF 171
Filters, quadrature mirror 171
Filters, smoothing 25
Filters, two-channel biorthogonal filter bank 179
Finer scale resolution 190
Finer time resolution 188
Finite element method 294
Finite-energy function 90
FIR filters 114 156 172
First-kind integral equation 268
FIWT 196
Fourier method 31
Fourier series 31
Fourier series kernel 34
Fourier transform 35
Fps 249
frequency scaling 38
Frequency shifting 38 63
Functional 5
Gabor transform 61
Galerkin method 272 274 279
Gaussian function 42 103
Generalized linear phase 171
Generalized self-similarity tree 244
Gibb’s phenomenon 50
Global basis 272
Graphical display 132
GST 237
Haar 96
Haar basis 13
Haar wavelet 105
Half-band filter 172
Hard thresholding 216
Hat function 84
HBF 172
Hermitian matrix 22
Hierarchical methods 294
Hierarchical wavelet decomposition 211
High frequency methods 294
Highpass filter 25
Histogram thresholding 248
Huffman code 235
Identity matrix 19
IIR filters 114 172
Image coding 235
Image compression 210 235
Image visualization 210
Impedance matrix 271
Inner product 8
Integral equations 268
Integral operator 272
Integral wavelet transform 67
interference suppression 210 219
Interoctave approximation subspaces 194
Interoctave parameter 190
Interoctave scales 190
Interpolation 144 147
Interpolator 145
Interpolatory representation 103
Interpretations 74
Intervallic wavelets 281
Inverse 19
Inverse wavelet transform 69
Inversion formula 61
Iteration method 132
IWT 67
Knot sequence 281
Linear function 197
Linear operator 272
Linear phase 171
Linear spaces 5
Linear spline 159 162
Linear transformation 18
Linearity 37 62
Local basis 13 272
Logarithmic division 220
Lossy coding 235
Lowpass filter 25 102
Mammogram 244
Marching algorithm 257
Marginal properties 80
Matrix, determinant 19
Matrix, eigenmatrix 19
Matrix, eigensystem 19
Matrix, eigenvalue 19
Matrix, eigenvectors 20
Matrix, hermitian 22
Matrix, identity 19
Matrix, inverse 19
Matrix, minor 19
Matrix, singular 19
Matrix, sparse 273
Matrix, transpose 18
Matrix, unitary 23
MCCS 250
Mean square error 16
Medical image visualization 252
Method of moments 268 272
Meyer wavelet 119
Meyer Wavelet, comer smoothing functions 120
Microcalcifications 244
Minor 19
MOM 268
Moment property 200
Moments 38
Morlet wavelet 71
Moving Average 24
MRA 89 151
MRA space 103
Multicarrier communication systems 210 249
Multigrid 294
Multiresolution analysis 89
Multiresolution spaces 89
Multivoice per octave 187
Music signal 204
MVPO 187
NEG 238
Neural network 223
noise reduction 210
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