DocumentCode :
1190599
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
Volume :
53
Issue :
1
fYear :
2005
Firstpage :
136
Lastpage :
146
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;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/TSP.2004.838936
Filename :
1369657
Link To Document :
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