The spectral signal processing suite

ABSTRACT

A software suite written in the Java programming language for the postprocessing of Chebyshev approximations to discontinuous functions is presented. It is demonstrated how to use the package to remove the effects of the Gibbs-Wilbraham phenomenon from Chebyshev approximations of discontinuous functions. Additionally, the package is used to postprocess Chebyshev collocation and Chebyshev super spectral viscosity approximations of hyperbolic partial differential equations. The postprocessing method is the Gegenbauer reconstruction procedure. The Spectral Signal Processing Suite is the first publicly available package that implements the procedure. State-of-the-art techniques are used to implement the algorithms with efficiency while reducing round-off error.

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.8 Partial Differential Equations
          Subjects: Spectral methods

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.2 Approximation
      G.1.8 Partial Differential Equations
          Subjects: Spectral methods

General Terms:
Algorithms

Keywords:
Gegenbauer postprocessing, Gibbs-Wilbraham phenomenon, Java, chebyshev, edge detection