Detecting derivative discontinuity locations in piecewise continuous functions from Fourier spectral data

Dennis Cates, Anne Gelb

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We present a method that uses Fourier spectral data to locate jump discontinuities in the first derivatives of functions that are continuous with piecewise smooth derivatives. Since Fourier spectral methods yield strong oscillations near jump discontinuities, it is often difficult to distinguish true discontinuities from artificial oscillations. In this paper we show that by incorporating a local difference method into the global derivative jump function approximation, we can reduce oscillations near the derivative jump discontinuities without losing the ability to locate them. We also present an algorithm that successfully locates both simple and derivative jump discontinuities.

Original languageEnglish (US)
Pages (from-to)59-84
Number of pages26
JournalNumerical Algorithms
Volume46
Issue number1
DOIs
StatePublished - Sep 1 2007

Keywords

  • Centered difference methods
  • Derivative jump discontinuities
  • Edge detection
  • Filtering
  • Fourier data

ASJC Scopus subject areas

  • Applied Mathematics

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