Title :
Iterative methods based on polynomial interpolation filters to detect discontinuities and recover point values from Fourier data
Author :
Wei, Musheng ; De Pierro, Alvaro R. ; Jiahong Yin
Author_Institution :
Dept. of Math., East China Normal Univ., Shanghai, China
Abstract :
In previous papers, we proposed new filters based on polynomial interpolation to approximate the point values of a piecewise smooth function f on [0,1] from its Fourier coefficients and derived error estimates. We proved that if all the discontinuity points of f are nodes, we can reconstruct point values of f accurately, even close to the discontinuities. We use the new filters to develop iterative methods for detecting the discontinuity points and, therefore, accurately approximate the point values of the function from its Fourier coefficients.
Keywords :
Fourier analysis; filtering theory; interpolation; iterative methods; piecewise polynomial techniques; Fourier coefficient; iterative method; piecewise smooth function; polynomial interpolation filter; recover point values; Convergence; Discrete Fourier transforms; Filters; Fourier transforms; Image reconstruction; Interpolation; Iterative methods; Mathematics; Polynomials; Signal processing;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2004.838936