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Wornell G. — Signal Processing with Fractals: A Wavelet Based Approach
Wornell G. — Signal Processing with Fractals: A Wavelet Based Approach



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Название: Signal Processing with Fractals: A Wavelet Based Approach

Автор: Wornell G.

Аннотация:

Fractal geometry and recent developments in wavelet theory are having an important impact on the field of signal processing. Efficient representations for fractal signals based on wavelets are opening up new applications for signal processing, and providing better solutions to problems in existing applications. Signal Processing with Fractals provides a valuable introduction to this new and exciting area, and develops a powerful conceptual foundation for understanding the topic. Practical techniques for synthesizing, analyzing, and processing fractal signals for a wide range of applications are developed in detail, and novel applications in communications are explored.


Язык: en

Рубрика: Математика/Численные методы/Вейвлеты, обработка сигналов/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 177

Добавлена в каталог: 05.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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($\lambda$) 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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