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Hubbard B. Ч The World According to Wavelets: The Story of a Mathematical Technique in the Making
Hubbard B. Ч The World According to Wavelets: The Story of a Mathematical Technique in the Making

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Ќазвание: The World According to Wavelets: The Story of a Mathematical Technique in the Making

јвтор: Hubbard B.

јннотаци€:

I own the very first (French) edition of Mrs. Barbara's book.

It is nice reading, but not so fun as some would say.

It has some advanced calculus level math ( Fourier transform ) and treats mainly Haar wavelets.

As an introduction to the subject it is quite adequate, but if you need/want something more go elsewhere.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1996

 оличество страниц: 275

ƒобавлена в каталог: 26.04.2014

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
"Hat" notation      96 103
$L^{2}$ (space)      133 168 176Ч177 185
Adaptive time segmentation      78Ч80
Adaptive windowed Fourier analysis      see "Malvar wavelets"
Adelson, Edward      42 45 47 62Ч63 139 162 187 188 192Ч193
Alessandro      see "d'Alessandro Christophe"
Amplitude      99
Analog      18
Analytical Theory of Heat      7Ч8 14Ч15
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      55Ч56 61
Artifacts, motion, reduction of, using wavelets      53Ч54
Astronomy      54 125
Atomic decompositions      26
Balian, Roger      29 36 78
Banach, Stefan      182
Barlaud, Michel      69Ч70
Basis      56 127Ч128 232Ч233 see
Battle Ч Lemarie spline functions      45 164
Battle, Guy      36 45
Benzi, Roberto      56
Berger, Jonathan      84
Best basis      81Ч86 88 136 194 201 202 205Ч207
Beylkin, Gregory      61 70
Bijaoui, Albert      54
Biorthogonal wavelets      69 80 196Ч197
Biot, Jean-Baptiste      109
Birkhoff, George      113
Bishop, Peter      187
Bit      64
Brahms      3 83Ч84
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      133Ч135
Coefficients, computing in orthonormal basis      126 129Ч133
Coefficients, computing with integrals      30Ч33 98 114Ч116 126 131Ч133
Coefficients, filter coefficients      159
Cohen, Albert      78
Coherent structures      72
Coifman, Ronald      3 36 75 77Ч78 85
Coifman, Ronald, Best Basis (including Brahms)      81 83Ч84
Coifman, Ronald, fast algorithms      40
Coifman, Ronald, matrix compression      70Ч71
Compact support      45 47 48 140 161
Compact transforms      189 190
Complex conjugate      136 226 232
Complex exponential      102
complex numbers      101Ч102 214Ч215
Complex-valued vectors, scalar product of      136
Complex-valued wavelets      75
Compression      64Ч65 67Ч68 78 162 188Ч189 198 203 see
Compression, comparing methods difficult      70
Compression, matrices      70Ч71
Compression, most signals not compressible      67
Compression, random signal incompressible      65Ч67
Compression, wavelets and      33 63 68Ч71 83
Computers      18 20 26 29 46 72 74Ч75 117 123 192Ч193
Constant Q filtering      62
Continuous wavelet transform      34Ч36 61 74Ч75 80 81 124Ч125 126 196
Continuous wavelet transform, aesthetics of      74
Continuous wavelet transform, formula and fast algorithms      124Ч125
Convergence      104Ч113
Convergence, easier proof of convergence of Fourier series      106 232Ч235
Convergence, pointwise      106
Convergence, Siegel, Carl, and small divisor problem      109
Convergence, small divisors and stability of solar system      107Ч113
Convergence, uniform      106
Convergence, weak      229
Convolutions, definition      157Ч158
Convolutions, wavelet transform and      158Ч161
Cooley, J.W.      117
Correlation      32 81Ч82
Cosine      212
Cousin, V.      5 6
Critical sampling      34 193
Crossword puzzles      82
D'Alembert      11
d'Alessandro, Christophe      80 203
Daubechies wavelets      45Ч48 149 163 194 195 203
Daubechies, Ingrid, compression and wavelets      63 68Ч69 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 134Ч135
Daubechies, Ingrid, redundance      36
Daubechies, Ingrid, time-frequency decompositions with wavelets      48Ч49
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      12Ч13
Delambre, Jean-Baptiste      11
Delprat, Nathalie      125
Delta function      see "Dirac $\delta$-function"
Denoising, Best Basis and Brahms recording      83Ч85
Denoising, defining noise      56
Denoising, new questions      85
Denoising, restoring singularities      52
Denoising, skeletons and      125
Denoising, wavelet maxima      59Ч61
Denoising, wavelet thresholding, Donoho and Johnstone      56-59
Denoising, wavelet thresholding, other      59Ч61
DeVore, Ronald      59
Differential equations      7Ч8 11Ч15 22 46 73 107
Digital technology      18Ч20
Dilation      41
Dimensionality reduction      189
Dirac $\delta$-function (delta function)      168 230 233
Dirac basis      168
Dirichlet, Gustave Lejeune      8 106 230
Discrete cosine transform      161
Discrete transforms      74Ч75 80 125 126 136
Distributions      107 182 184 229Ч230
Divergence      105 107
Donoho, David      56Ч59 61 85 89
Donovan, George      163
Dot product      see "Scalar product"
Dyadic      125
Dynamical systems      46 113
e (number)      101Ч102
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)      29Ч30 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      74Ч75 194
Farge, Marie, interpreting coefficients      62 74
Farge, Marie, multiresolution analysis, importance of      39
Farge, Marie, wavelets and turbulence      71Ч72 78 189
Fast Fourier transform (FFT)      117Ч123
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      119Ч123
Fast wavelet transform (FWT)      42Ч45 86 154Ч161
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      156Ч157 159Ч161
Fast wavelet transform (FWT), importance of      40 45 139
Fast wavelet transform (FWT), scaling function in      42Ч44 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 187Ч192
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      138Ч139 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      7Ч8 11Ч19 51
Fourier analysis, solving differential equations      12Ч15
Fourier analysis, time information hidden      22Ч23 53
Fourier analysis, unsuited to nonlinear problems      73Ч74
Fourier coefficients      9 12Ч13 17Ч18 97Ч100 104 114Ч116 185
Fourier series of function that decreases at infinity      231
Fourier series, convergence of      104Ч113
Fourier series, formulas for      97Ч98
Fourier series, formulas for, using complex exponentials      102
Fourier transform      9 15 29 82 96Ч103 192 200 see "Fourier "Windowed "Fourier
Fourier transform of periodic function      227Ч230
Fourier transform of sequence of numbers      147 227Ч230
Fourier transform, "hat" notation      96 103
Fourier transform, amplitude      99
Fourier transform, computing      118Ч119
Fourier transform, formulas for:      101
Fourier transform, formulas for:, using complex exponentials      102 220
Fourier transform, phase      99Ч100
Fourier transform, physical reality of      15 62
Fourier, Joseph      5Ч9 11 14Ч15 17 117 181
Fractal wavelets      163Ч164
Fractals      11 54Ч56 59
frames      196
Frazier, Michael      3 20 70 219
Freeman, William T.      193
Frequency of digital filter      151
Frequency of wavelets, not precise      31 198Ч199
Frequency, doubles, with octaves      19
Frequency, measured: in hertz      96
Frequency, measured: in radians      212Ч213
Frequency, spatial      16 96Ч97
Frequency, variables representing      97Ч98 118
Frisch, Uriel      54Ч56
Function spaces      127 129 181Ч182 184Ч185 see
Function spaces, access to: with Fourier analysis      185Ч186
Function spaces, access to: with wavelets      26 186
Functions      9Ч10
Functions as point or vector in infinite-dimensional space      103 127Ч129 183Ч185
Functions, analyzing functions      15 126
Functions, history (changing definition)      10Ч11 181Ч186
Functions, length of      129 133
Functions, notation: f or f(x)      102Ч103
Functions, zeta function      183Ч184
FWT      see "Fast wavelet transform"
Gabor transforms      26Ч28 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      22Ч23
Gabor, Dennis, windowed Fourier analysis      23Ч24 26 31 187 203
Galand, C. (and quadrature mirror filters)      147 162
Gauss, Carl Friedrich (and fast Fourier transform)      20 117 121Ч122
Gelfand, Israel      107 182 184
Geronimo, Jeffrey S.      163Ч164
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      24Ч25 29Ч30 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 $(\hbar)$      179
Haar function      see "Haar wavelet"
Haar scaling function      141Ч143 145 148 149 156Ч157 159Ч161
Haar wavelet      36 141 152 156Ч157 159Ч161 163 196
Hardin, Douglas P.      163
Hausdorff, Felix      182
Healy, Dennis Jr.      53 70 78
Hearing      62Ч63
Heat diffusion      7Ч8 11Ч15 17
Heaviside, Oliver (and distributions)      184
Heisenberg boxes      168 205Ч207
Heisenberg cells      see "Heisenberg boxes"
Heisenberg uncertainty principle in communication theory and signal processing      48Ч51 165Ч170 171 199
Heisenberg uncertainty principle in quantum mechanics      49 51 171 176 178 180
Heisenberg uncertainty principle, proof      136 224Ч226
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 68Ч70 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      64Ч65
Inner product      126 see
Innocent, Jean-Michel      125
Integrals      see also "Lebesgue integral" "Riemann
Integrals, comparison of Lebesgue and Riemann integrals      216Ч219
Integrals, computing coefficients with      30Ч33 98 114Ч116 131Ч133
Integrals, measuring continuous probability spaces      173Ч174
Integrals, relationship with scalar products      131Ч133
Integrals, zero, of wavelet      32 36
Integration      118
Isometry      225
Iterated Function Systems      146
iterations      46Ч47 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      65Ч68
Kolmogorov, Andrei, definition of random      65
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