Journal ArticleDOI
Multiscale Wiener filter for the restoration of fractal signals: wavelet filter bank approach
Bor-Sen Chen,Chin-Wei Lin +1 more
TLDR
A filter bank design based on orthonormal wavelets and equipped with a multiscale Wiener filter can be applied to treat the signal restoration problem for nonstationary 1/f fractal signals.Abstract:
A filter bank design based on orthonormal wavelets and equipped with a multiscale Wiener filter is proposed in this paper for signal restoration of 1/f family of fractal signals which are distorted by the transmission channel and corrupted by external noise. First, the fractal signal transmission process is transformed via the analysis filter bank into multiscale convolution subsystems in time-scale domain based on orthonormal wavelets. Some nonstationary properties, e.g., self-similarity, long-term dependency of fractal signals are attenuated in each subband by wavelet multiresolution decomposition so that the Wiener filter bank can be applied to estimate the multiscale input signals. Then the estimated multiscale input signals are synthesized to obtain the estimated input signal. Some simulation examples are given for testing the performance of the proposed algorithm. With this multiscale analysis/synthesis design via the technique of the wavelet filter bank, the multiscale Wiener filter can be applied to treat the signal restoration problem for nonstationary 1/f fractal signals. >read more
Citations
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Journal ArticleDOI
Self-Similarity: Part I—Splines and Operators
Michael Unser,Thierry Blu +1 more
TL;DR: It is proved that the corresponding variational (or smoothing) spline estimator is a cardinal fractional spline of order 2gamma, which admits a stable representation in a B-spline basis.
Adaptive wavelet network control design for nonlinear systems
TL;DR: It is shown that the effects of approximation errors and external disturbances can be attenuated to a specific attenuation level by the proposed adaptive wavelet network control scheme.
Journal ArticleDOI
Perfect reconstruction versus MMSE filter banks in source coding
K. Gosse,P. Duhamel +1 more
TL;DR: This paper solves the problem of minimizing the reconstruction distortion, which, in the most general case, is the sum of two terms: a first one due to the non-PR property of the FB and the other being due to signal quantization in the subbands.
Journal ArticleDOI
Maximum likelihood parameter estimation of F-ARIMA processes using the genetic algorithm in the frequency domain
TL;DR: This work aims to treat the parameter estimation problem for fractional-integrated autoregressive moving average (F-ARIMA) processes under external noise from the frequency domain perspective and develops an estimation scheme based on the GA to solve this problem.
Journal ArticleDOI
Analytical formulation of the fractal dimension of filtered stochastic signals
TL;DR: The aim of this study was to investigate the effects of a linear filter on the regularity of a given stochastic process in terms of the fractal dimension.
References
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Journal ArticleDOI
A theory for multiresolution signal decomposition: the wavelet representation
TL;DR: In this paper, it is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2 /sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions.
Journal ArticleDOI
Orthonormal bases of compactly supported wavelets
TL;DR: This work construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity, by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction.
Journal ArticleDOI
Fractional Brownian Motions, Fractional Noises and Applications
Journal ArticleDOI
The wavelet transform, time-frequency localization and signal analysis
TL;DR: Two different procedures for effecting a frequency analysis of a time-dependent signal locally in time are studied and the notion of time-frequency localization is made precise, within this framework, by two localization theorems.
Journal ArticleDOI
Wavelets and signal processing
Olivier Rioul,Martin Vetterli +1 more
TL;DR: A simple, nonrigorous, synthetic view of wavelet theory is presented for both review and tutorial purposes, which includes nonstationary signal analysis, scale versus frequency,Wavelet analysis and synthesis, scalograms, wavelet frames and orthonormal bases, the discrete-time case, and applications of wavelets in signal processing.