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Radunovic D.P. — Wavelets: From Math to Practice
Radunovic D.P. — Wavelets: From Math to Practice

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Название: Wavelets: From Math to Practice

Автор: Radunovic D.P.

Аннотация:

The method of wavelet transforms is one key tool in signal processing and control. Modern wavelet theory defines outlines for construction of wavelets and transformations using them. It gives rules that one has to obey to get a wavelet basis with desired properties, meaning that everyone can create a wavelet adequate for the given task. This book helps to understanding this rules. In seven chapters, the book gives a concise understanding of the theory of wavelets, explains how to compute them in practise and finally presents typical applications of wavelets and how they work. The book is written for graduate students and practising Engineers of electrical communications, signal processing and control.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2009

Количество страниц: 163

Добавлена в каталог: 23.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathcal{Z}$, $\mathcal{R}$, $\mathcal{C}$      9
Aliasing      125
Basis, biorthogonal      11 96
Basis, complete orthonormal      10
Basis, frame      11
Basis, orthonormal      10
Basis, Riesz      11 97
Battle — Lemarie wavelet      104
Biorthogonal wavelet      40 51 96 104 146
Cascade algorithm      81
Characteristic function      3 15 24 118 124
Coiflet wavelet      95
Compact support      5 29
Compression      90
Condition, approximation of order r      61 69 146
Condition, biorthogonality      146
Condition, eigenvalues      146
Condition, orthogonality      137 139 145
Condition, perfect reconstruction      144
Convolution, discrete      18
Convolution, function      15 98
Convolution, signal      126
Convolution, theorem      16 19
Cyclic matrix      19
Daubechies      5
Daubechies filter      141 142
Daubechies function      53
Daubechies wavelet      54 93
Dilatation      36
Dilatation equation      38 96
Dilatation equation, cascade algorithm      43 57 70
Dilatation equation, coefficients      56
Dilatation equation, Fourier transform      60
Dilatation equation, recursion      66
Dirac function      24 109
Double shift orthogonality      43 136 146
Eigenfunctions, convolution operator      15
Eigenfunctions, differential operator      14
Eigenfunctions, finite difference operator      14
Energy norm      7 10 14
Energy norm, discrete      9
Filter      126
Filter, analysis      131
Filter, averaging      128
Filter, bank      131 135
Filter, causal      126
Filter, delay      127
Filter, differing      129
Filter, FIR      127
Filter, frequency response      59 126
Filter, halfband      140
Filter, Highpass      129
Filter, HR      127
Filter, invertible      130
Filter, Lowpass      128
Filter, matrix      18 64 126
Filter, maxflat      142
Filter, mirror symmetry      131 137
Filter, perfect reconstruction      131 136
Filter, power spectral response      139
Filter, synthesis      131
FOURIER      2
Fourier analysis      13
Fourier coefficient      10
Fourier complex series      13
Fourier discrete series      21
Fourier discrete transform      21
Fourier inverse transform      15
Fourier matrix      18
Fourier series      10 20
Fourier short time transform      26
Fourier transform      15 20
Fourier trigonometric series      13
frequency      13
Frequency range      124
Gramm determinant      9
Haar      3
Haar filter bank      134
Haar wavelet      49
Harmonic analysis      13
Inner product      7 8
Least-squares approximation      7
Lifting      111
Mexican hat      117
Meyer wavelet      118
Modulation      16 28
Morlet wavelet      116
Multiresolution      4 35
Multiresolution, decomposition      40
Nyquist rule      32
Nyquist speed      124
Operator, downsampling      64 131
Operator, upsampling      132
Parseval equality      10 16 20 30
Parseval equality, generalised      10
Poisson summation formula      125
Pre-filtering      91
Pyramid algorithm      45 97
Pyramid algorithm, analysis      85
Pyramid algorithm, synthesis      86 97
Sampling theorem      123
Scaling      28
Scaling function      36
Scaling function, box function      48 98
Scaling function, frequency domain      59
Scaling function, graph      92
Scaling function, interpolation      106
Scaling function, orthogonality      43 61
Scaling function, roof function      50
Scaling function, smoothness      82
Shannon function      124
Shannon wavelet      117
signal      18 123 149
Signal, analysis      84
Signal, processing      123
Signal, synthesis      84
Signal, two-dimensional      123 149
Space, $\mathcal{L}_{2}[a, b]$      7
Space, approximation $\mathcal{V}_{j}$      36
Space, strictly normed      9
Space, wavelet $\mathcal{W}_{j}$      37
Spectral analysis      14
Spectrum      14
Spline, B-spline      53 98
Spline, box function      48 98
Spline, derivative      101
Spline, roof function      50 100
Symlet wavelet      94
Transform, discrete wavelet      83
Transform, FFT      21
Transform, Short Time Fourier      26
Transform, wavelet      29 45 86
Transform, z-transform      19
Translation      28 37
Two-dimensional wavelets      119
Uncertainty principle      27
Wavelet      3 5 29 38 55
Wavelet, accuracy      71
Wavelet, approximation      74
Wavelet, coefficients      75
Wavelet, discrete      33
Wavelet, discrete transform      83
Wavelet, equation      38 56 96
Wavelet, fast transform      85
Wavelet, first generation      111
Wavelet, frequency domain      62
Wavelet, graph      92
Wavelet, interpolation      105 109
Wavelet, inverse transform      30
Wavelet, lazy      111
Wavelet, moment      41 73
Wavelet, multiwavelet      52
Wavelet, orthogonality      44
Wavelet, packet analysis      93
Wavelet, properties      119 121
Wavelet, second generation      111
Wavelet, semiorthogonal      103
Wavelet, space      37
Wavelet, transform      29 45
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