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| Wornell G. - Signal Processing with Fractals: A Wavelet Based Approach |
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| Предметный указатель |
1/f noise 59
1/f process 30-32
1/f process, Barnes - Allan model 37 42
1/f process, correlation function 45
1/f process, Corsini - Saletti synthesis 46
1/f process, Cramer - Rao bounds 69
1/f process, distribution of time-constants model 43
1/f process, examples 33
1/f process, fractal dimension 33
1/f process, fractal dimension estimation 64
1/f process, frequency-domain characterization 41
1/f process, Karhunen - Loeve-type expansions 46
1/f process, Keshner model 44
1/f process, mathematical definition 41
1/f process, maximum likelihood parameter estimation 63
1/f process, measured power spectra 32
1/f process, parameter estimation 120
1/f process, pole-zero behavior 45
1/f process, RC transmission line model 44
1/f process, sample paths 32
1/f process, smoothing (noise reduction) 72
1/f process, spectrum 41
1/f process, spectrum estimation 64
1/f process, state variables 45
1/f process, synthesis filter 62
1/f process, Van der Ziel model 43
1/f process, wavelet coefficient correlation 50-51
1/f process, wavelet coefficient stationarity properties 50
1/f process, wavelet coefficient variances 51
1/f process, wavelet coefficients, ideal bandpass basis 52
1/f process, wavelet-based analysis 50
1/f process, wavelet-based models 46
1/f process, wavelet-based synthesis 47
1/f process, wavelet-based synthesis, regularity issues 49
1/f process, whitening filter 61-62
Autoregressive moving-average (ARMA) models 35 43
Bandpass filter, ideal, continuous-time 11
Barnes - Allan process 37 42 45
Bihomogeneous signal 95
Brownian motion 31 36 38
Characteristic sequence 108
Characteristic sequence, synthesis 110
Communication channel models 113
Conjugate quadrature filter (CQF) 25-27
Differentiation in scale 135
Discrete wavelet transform 21
Discrete wavelet transform, analysis algorithm 22
Discrete wavelet transform, complexity 22
Discrete wavelet transform, data length and resolution effects 23
Discrete wavelet transform, synthesis algorithm 22
Euler - Cauchy equations 136
Filter bank, octave band 13
Fourier transform, definition, continuous-time 10
Fourier transform, definition, discrete-time 21
Fractal dimension 33
Fractal dimension, estimation 64
Fractal dimension, estimator performance 71
Fractal dimension, estimator performance bounds 69
Fractal modulation, analog data 124
Fractal modulation, choice of fractal dimension 118
Fractal modulation, digital data 121
Fractal modulation, discrete-time implementation 117 122-124
Fractal modulation, finite-length messages 118
Fractal modulation, performance 122 126
Fractal modulation, power efficiency 123
Fractal modulation, receiver 120
Fractal modulation, requirements 114
Fractal modulation, spectral efficiency 116
Fractal modulation, spectral matching 120
Fractal modulation, transmitter 115
Fractional Brownian motion 30 36
Fractional Brownian motion, correlation function 38
Fractional Brownian motion, definition 38
Fractional Brownian motion, derivative 39
Fractional Brownian motion, increments 38
Fractional Brownian motion, limitations 40
Fractional Brownian motion, self-similarity parameter 38
Fractional Brownian motion, synthesis 39 139
Fractional Brownian motion, uniqueness 40
Fractional Brownian motion, variance 40
Fractional calculus 45
Fractional Gaussian noise 36
Fractional Gaussian noise, correlation structure 39
Generating sequence 99
Highpass filter, ideal, discrete-time 22
Homogeneous signal 95
Homogeneous signal, bihomogeneous signal 95
Homogeneous signal, characteristic sequence 108
| Homogeneous signal, discrete-time 109
Homogeneous signal, energy-dominated 96 97
Homogeneous signal, equivalence class 98
Homogeneous signal, examples 97 105
Homogeneous signal, Fourier transform 97 103
Homogeneous signal, fractal dimension 104
Homogeneous signal, generating sequence 99
Homogeneous signal, Hilbert space 100
Homogeneous signal, input to LTSI( ) system 138
Homogeneous signal, periodicity-dominated 107 118
Homogeneous signal, power spectrum 103-105
Homogeneous signal, power-dominated 96 103
Homogeneous signal, randomly-generated 105
Homogeneous signal, regularity 104
Homogeneous signal, time-frequency portrait 107
Homogeneous signal, wavelet expansion 98
Infrared catastrophe 35
Iterated function system 110
Johnson noise 60
Laplace transform 130-132
Linear scale-invariant system 132
Linear scale-invariant system, convolution property 133
Linear scale-invariant system, eigenfunctions 133
Linear scale-invariant system, generalized class 136
Linear scale-invariant system, lagged-impulse response 132
Linear scale-invariant system, system function 134
Linear system 131
Linear time- and scale-invariant system 137
Linear time- and scale-invariant system, dyadic approximation 143
Linear time- and scale-invariant system, wavelet representation 140
Linear time-invariant system 131
Linear time-invariant system, impulse response 131
Long-term dependence 39
Lorenzian spectra 43
Lowpass filter, ideal, continuous-time 19
Lowpass filter, ideal, discrete-time 22
Mellin transform 130 134
Mellin transform, inverse formula 134
Multiresolution signal analysis 16
Multiresolution signal analysis, characterization 17
Multiresolution signal analysis, detail signal 20
Multiresolution signal analysis, perfectly bandlimited 19
Nearly-1/f process, spectrum 47
Nearly-1/f process, wavelet-based synthesis 47
Nearly-1/f processes 30 43
Poisson formula 12
Regularity 12
Scale-differential equations 135
Scaling function 18
Scaling function, ideal lowpass 19
Self-similar basis 96 99
Self-similar basis, example 101
Self-similar system 130
Shot noise 60
Spectral efficiency 114
Stable distributions 35
Statistical self-similarity 31
Thermal noise 60
Time-frequency analysis 14
Ultraviolet catastrophe 35
Wavelet bases 9
Wavelet bases, Battle - Lemarie 27
Wavelet bases, construction of 25
Wavelet bases, dyadic 11
Wavelet bases, example lacking multiresolution analysis 12
Wavelet bases, examples 26
Wavelet bases, filter bank interpretation 13
Wavelet bases, multiresolution analysis interpretation 16
Wavelet bases, nondyadic 27
Wavelet bases, orthonormal 11
Wavelet bases, synthesis/analysis equations 11
Wavelet bases, useful identity 15
Wavelet bases, vanishing moments 26-27
Wavelet bases, wavelet 11
Wavelet, basic 11
Wavelet, basic (or "mother") 20
Wavelet, Battle - Lemarie 27
Wavelet, Daubechies 27
Wavelet, father 18
Wavelet, frame 10
Wavelet, Haar 26
Wavelet, ideal bandpass 11 13 15 20 26 28
Wavelet, mother 11
Wavelet, scaling function 18
Wavelet-based modeling, Dow Jones Industrial Average 54
Wavelet-based modeling, heartbeat interarrival data 55
White Gaussian noise 31 35
Wiener process 31 35 38
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