A Fast Wavelet Algorithm for Analyzing One- Dimensional Signal Processing and Asymptotic Distribution of Wavelet Coefficients With Numerical Example and Simulation, By Mahmoud Afshari

Research

Title	A Fast Wavelet Algorithm for Analyzing One- Dimensional Signal Processing and Asymptotic Distribution of Wavelet Coefficients With Numerical Example and Simulation
Type	Article
Keywords	—
Journal	COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
DOI	—
Researchers	Mahmoud Afshari (First researcher)

Abstract

In this article, we consider a sample point (tj, sj) including a value sj== f(tj) at height sj and abscissa (time or location) tj . We apply wavelet decomposition by using shifts and dilations of the basic H?ar 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.