Iterative methods based on polynomial interpolation filters to detect discontinuities and recover point values from Fourier data

Authors:
Musheng Wei;A.R. De Pierro;Jiahong Yin
Affiliations:
Dept. of Math., East China Normal Univ., Shanghai, China;-;-
Venue:
IEEE Transactions on Signal Processing
Year:
2005

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Iterative methods based on spline approximations to detect discontinuities from Fourier data

Journal of Computational and Applied Mathematics

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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.