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| Ïîèñê ïî óêàçàòåëÿì |
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| Hubbard B. — The World According to Wavelets: The Story of a Mathematical Technique in the Making |
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| Ïðåäìåòíûé óêàçàòåëü |
"Hat" notation 96 103
 (space) 133 168 176—177 185
Adaptive time segmentation 78—80
Adaptive windowed Fourier analysis see "Malvar wavelets"
Adelson, Edward 42 45 47 62—63 139 162 187 188 192—193
Alessandro see "d'Alessandro Christophe"
Amplitude 99
Analog 18
Analytical Theory of Heat 7—8 14—15
Apery, Roger, and zeta function 184
Argoul, F. 54
Arneodo, Alain 54 55 59
Arnold, Vladimir, and KAM theorem 113
Artifacts 141 197
Artifacts, danger of, with wavelets 55—56 61
Artifacts, motion, reduction of, using wavelets 53—54
Astronomy 54 125
Atomic decompositions 26
Balian, Roger 29 36 78
Banach, Stefan 182
Barlaud, Michel 69—70
Basis 56 127—128 232—233 see
Battle — Lemarie spline functions 45 164
Battle, Guy 36 45
Benzi, Roberto 56
Berger, Jonathan 84
Best basis 81—86 88 136 194 201 202 205—207
Beylkin, Gregory 61 70
Bijaoui, Albert 54
Biorthogonal wavelets 69 80 196—197
Biot, Jean-Baptiste 109
Birkhoff, George 113
Bishop, Peter 187
Bit 64
Brahms 3 83—84
Burt, Peter 42 45 47 139 162
BYTE 64
Calderon, A.P. 186
Cayley, Arthur 122
Chameleon effect 55
Chaos 11 46
Ciliberto, S. 56
Coefficients 30 see "Wavelet
Coefficients, computing in non-orthogonal basis 133—135
Coefficients, computing in orthonormal basis 126 129—133
Coefficients, computing with integrals 30—33 98 114—116 126 131—133
Coefficients, filter coefficients 159
Cohen, Albert 78
Coherent structures 72
Coifman, Ronald 3 36 75 77—78 85
Coifman, Ronald, Best Basis (including Brahms) 81 83—84
Coifman, Ronald, fast algorithms 40
Coifman, Ronald, matrix compression 70—71
Compact support 45 47 48 140 161
Compact transforms 189 190
Complex conjugate 136 226 232
Complex exponential 102
complex numbers 101—102 214—215
Complex-valued vectors, scalar product of 136
Complex-valued wavelets 75
Compression 64—65 67—68 78 162 188—189 198 203 see
Compression, comparing methods difficult 70
Compression, matrices 70—71
Compression, most signals not compressible 67
Compression, random signal incompressible 65—67
Compression, wavelets and 33 63 68—71 83
Computers 18 20 26 29 46 72 74—75 117 123 192—193
Constant Q filtering 62
Continuous wavelet transform 34—36 61 74—75 80 81 124—125 126 196
Continuous wavelet transform, aesthetics of 74
Continuous wavelet transform, formula and fast algorithms 124—125
Convergence 104—113
Convergence, easier proof of convergence of Fourier series 106 232—235
Convergence, pointwise 106
Convergence, Siegel, Carl, and small divisor problem 109
Convergence, small divisors and stability of solar system 107—113
Convergence, uniform 106
Convergence, weak 229
Convolutions, definition 157—158
Convolutions, wavelet transform and 158—161
Cooley, J.W. 117
Correlation 32 81—82
Cosine 212
Cousin, V. 5 6
Critical sampling 34 193
Crossword puzzles 82
D'Alembert 11
d'Alessandro, Christophe 80 203
Daubechies wavelets 45—48 149 163 194 195 203
Daubechies, Ingrid, compression and wavelets 63 68—69 196
Daubechies, Ingrid, early involvement with wavelets 45 47
Daubechies, Ingrid, fast wavelet transform 155
Daubechies, Ingrid, matrix compression 71
Daubechies, Ingrid, multiresolution 39
Daubechies, Ingrid, noise 52
Daubechies, Ingrid, notation 142
Daubechies, Ingrid, pure mathematics and wavelets 52
Daubechies, Ingrid, quantization 69 134—135
Daubechies, Ingrid, redundance 36
Daubechies, Ingrid, time-frequency decompositions with wavelets 48—49
Daubechies, Ingrid, vanishing moments 161 198
Daugman, John 188
DCT see "Discrete cosine transform"
de Moivre formula 101 119 214 215 235
De Moivre, Abraham 101
Decoupling 12—13
Delambre, Jean-Baptiste 11
Delprat, Nathalie 125
Delta function see "Dirac  -function"
Denoising, Best Basis and Brahms recording 83—85
Denoising, defining noise 56
Denoising, new questions 85
Denoising, restoring singularities 52
Denoising, skeletons and 125
Denoising, wavelet maxima 59—61
Denoising, wavelet thresholding, Donoho and Johnstone 56-59
Denoising, wavelet thresholding, other 59—61
DeVore, Ronald 59
Differential equations 7—8 11—15 22 46 73 107
Digital technology 18—20
Dilation 41
Dimensionality reduction 189
Dirac -function (delta function) 168 230 233
Dirac basis 168
Dirichlet, Gustave Lejeune 8 106 230
Discrete cosine transform 161
Discrete transforms 74—75 80 125 126 136
Distributions 107 182 184 229—230
Divergence 105 107
Donoho, David 56—59 61 85 89
Donovan, George 163
Dot product see "Scalar product"
Dyadic 125
Dynamical systems 46 113
e (number) 101—102
Edison, Thomas 83
Egypt (and Fourier) 6
Einstein, Albert (speaking of Newton) 7
El Nino ocean current 53
Energy (of error) 135
Energy (of signal) 29—30 57 191 192 196
entropy 81 82
Epperson, Jay 70
Escudie, Bernard 124
Esteban, D. (and quadrature mirror filters) 147 162
Euler, Leonhard (and zeta function) 183
Event 172
Expectation 172
Exponential 102
Extended Self Similarity 56
| Faraday, Michael (on mathematical writing) xiii
Farge, Marie, choice of transform 76 200
Farge, Marie, choice of wavelet 74—75 194
Farge, Marie, interpreting coefficients 62 74
Farge, Marie, multiresolution analysis, importance of 39
Farge, Marie, wavelets and turbulence 71—72 78 189
Fast Fourier transform (FFT) 117—123
Fast Fourier transform (FFT), abuse of 21
Fast Fourier transform (FFT), alternative description 118
Fast Fourier transform (FFT), comparison with fast wavelet transform 161
Fast Fourier transform (FFT), discrete form of Fourier transform 118
Fast Fourier transform (FFT), history of 117 121
Fast Fourier transform (FFT), importance of 20 40 45 117
Fast Fourier transform (FFT), matrix form 119—123
Fast wavelet transform (FWT) 42—45 86 154—161
Fast wavelet transform (FWT), comparison with fast Fourier transform 161
Fast wavelet transform (FWT), concise 156
Fast wavelet transform (FWT), example with Haar scaling function and wavelet 156—157 159—161
Fast wavelet transform (FWT), importance of 40 45 139
Fast wavelet transform (FWT), scaling function in 42—44 154
Fast wavelet transform (FWT), speed of 45 139 155 161
Father function 41 see
FBI (Federal Bureau of Investigations) 83
Field, David J. 25 62 64 187—192
Filter coefficients 159
Filters 39 138 152 161
Filters, digital, frequencies of 147 151 230
Filters, high-pass filter 139 150 159
Filters, low-pass filter 138—139 147 159
Filters, shiftable filters 193
Filters, steerable filters 193
fingerprints 83
Fourier analysis see also "Fourier series" "Fourier "Fourier
Fourier analysis, quantum mechanics and 15 17 51
Fourier analysis, significance of 7—8 11—19 51
Fourier analysis, solving differential equations 12—15
Fourier analysis, time information hidden 22—23 53
Fourier analysis, unsuited to nonlinear problems 73—74
Fourier coefficients 9 12—13 17—18 97—100 104 114—116 185
Fourier series of function that decreases at infinity 231
Fourier series, convergence of 104—113
Fourier series, formulas for 97—98
Fourier series, formulas for, using complex exponentials 102
Fourier transform 9 15 29 82 96—103 192 200 see "Fourier "Windowed "Fourier
Fourier transform of periodic function 227—230
Fourier transform of sequence of numbers 147 227—230
Fourier transform, "hat" notation 96 103
Fourier transform, amplitude 99
Fourier transform, computing 118—119
Fourier transform, formulas for: 101
Fourier transform, formulas for:, using complex exponentials 102 220
Fourier transform, phase 99—100
Fourier transform, physical reality of 15 62
Fourier, Joseph 5—9 11 14—15 17 117 181
Fractal wavelets 163—164
Fractals 11 54—56 59
frames 196
Frazier, Michael 3 20 70 219
Freeman, William T. 193
Frequency of digital filter 151
Frequency of wavelets, not precise 31 198—199
Frequency, doubles, with octaves 19
Frequency, measured: in hertz 96
Frequency, measured: in radians 212—213
Frequency, spatial 16 96—97
Frequency, variables representing 97—98 118
Frisch, Uriel 54—56
Function spaces 127 129 181—182 184—185 see
Function spaces, access to: with Fourier analysis 185—186
Function spaces, access to: with wavelets 26 186
Functions 9—10
Functions as point or vector in infinite-dimensional space 103 127—129 183—185
Functions, analyzing functions 15 126
Functions, history (changing definition) 10—11 181—186
Functions, length of 129 133
Functions, notation: f or f(x) 102—103
Functions, zeta function 183—184
FWT see "Fast wavelet transform"
Gabor transforms 26—28 187 188
Gabor, Dennis, holography 22
Gabor, Dennis, importance of uncertainty principle in acoustics 49
Gabor, Dennis, limit of information transmissible 64
Gabor, Dennis, reservations about Fourier analysis 22—23
Gabor, Dennis, windowed Fourier analysis 23—24 26 31 187 203
Galand, C. (and quadrature mirror filters) 147 162
Gauss, Carl Friedrich (and fast Fourier transform) 20 117 121—122
Gelfand, Israel 107 182 184
Geronimo, Jeffrey S. 163—164
Gibbs' phenomenon 106
Gonnet, Caroline 125
Granlund, Goesta 187
Grasseau, G. 54
Gravitational waves, detection of 125
Grossmann, Alex, continuous wavelet transform 35
Grossmann, Alex, Daubechies 47
Grossmann, Alex, definition of wavelet a scholastic question 80
Grossmann, Alex, denoising 57
Grossmann, Alex, early involvement with wavelets 24—25 29—30 34 71
Grossmann, Alex, hearing and wavelets 62
Grossmann, Alex, influence of wavelets on interdisciplinary work 25
Grossmann, Alex, matrix compression 71
Grossmann, Alex, speed of computations 45
Guillemain, Philippe 125
H see "Planck's constant"
h bar  179
Haar function see "Haar wavelet"
Haar scaling function 141—143 145 148 149 156—157 159—161
Haar wavelet 36 141 152 156—157 159—161 163 196
Hardin, Douglas P. 163
Hausdorff, Felix 182
Healy, Dennis Jr. 53 70 78
Hearing 62—63
Heat diffusion 7—8 11—15 17
Heaviside, Oliver (and distributions) 184
Heisenberg boxes 168 205—207
Heisenberg cells see "Heisenberg boxes"
Heisenberg uncertainty principle in communication theory and signal processing 48—51 165—170 171 199
Heisenberg uncertainty principle in quantum mechanics 49 51 171 176 178 180
Heisenberg uncertainty principle, proof 136 224—226
Hermite, Charles 181
Hertz 18 96
High-pass filter see "Filters"
Hugo, Victor (on Fourier) 7
Hwang, Wen Liang (and wavelet maxima) 59 125
Hybrids see "Malvar wavelets" "Wavelet
Image processing 38 68—70 78 125 137 138 139 140 162
Infinite product 149
Information, Kolmogorov information content 65 67
Information, not to be confused with meaning 67
Information, quantifying 64—65
Inner product 126 see
Innocent, Jean-Michel 125
Integrals see also "Lebesgue integral" "Riemann
Integrals, comparison of Lebesgue and Riemann integrals 216—219
Integrals, computing coefficients with 30—33 98 114—116 131—133
Integrals, measuring continuous probability spaces 173—174
Integrals, relationship with scalar products 131—133
Integrals, zero, of wavelet 32 36
Integration 118
Isometry 225
Iterated Function Systems 146
iterations 46—47 86
Jacobi, Carl (on Fourier) 11
Jaffard, Stephane 55 186
Johnstone, Iain 56 59 61
Kam theorem 113
Kerkyacharian, Gerard 57
Koerner, T.W. 8 11 20 21
Kolmogorov, Andrei, compressibility of information 65—68
Kolmogorov, Andrei, definition of random 65
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