Filters , mollifiers and the computation of the Gibbs phenomenon

@inproceedings{Tadmor2007FiltersM,
  title={Filters , mollifiers and the computation of the Gibbs phenomenon},
  author={Eitan Tadmor},
  year={2007}
}
We are concerned here with processing discontinuous functions from their spectral information. We focus on two main aspects of processing such piecewise smooth data: detecting the edges of a piecewise smooth f , namely, the location and amplitudes of its discontinuities; and recovering with high accuracy the underlying function in between those edges. If f is a smooth function, say analytic, then classical Fourier projections recover f with exponential accuracy. However, if f contains one or… CONTINUE READING
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