Edge Detection Free Postprocessing for Pseudospectral Approximations

Pseudospectral Methods based on global polynomial approximation yield exponential accuracy when the underlying function is analytic. The presence of discontinuities destroys the extreme accuracy of the methods and the well-known Gibbs phenomenon appears. Several types of postprocessing methods have been developed to lessen the effects of the Gibbs phenomenon or even to restore spectral accuracy. The most powerful of the methods require that the locations of the discontinuities be precisely known. In this work we discuss postprocessing algorithms that are applicable when it is impractical, or difficult, or undesirable to pinpoint all discontinuity locations. keywords: Fourier, Chebyshev, Pseudospectral, Gibbs, Spectral filtering, Digital Total Variation filtering.