A Fast Wavelet Algorithm for Analyzing One-Dimensional Signal Processing and Asymptotic Distribution of Wavelet Coefficients With Numerical Example and Simulation |
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Authors: | M. Afshari |
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Affiliation: | 1. Department of Statistics and Mathematics , Persian Gulf University , Bushehr , Iran afshar@pgu.ac.ir |
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Abstract: | In this article, we consider a sample point (t j , s j ) including a value s j = f(t j ) at height s j and abscissa (time or location) t j . We apply wavelet decomposition by using shifts and dilations of the basic Häar transform and obtain an algorithm to analyze a signal or function f. We use this algorithm in practical to approximating function by numerical example. Some relationships between wavelets coefficients and asymptotic distribution of wavelet coefficients are investigated. At the end, we illustrate the results on simulated data by using MATLAB and R software. |
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Keywords: | Asymptotic distribution Estimation Fast wavelets Häar wavelets Multiresolution analysis Signal Wavelet coefficients |
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