Removing pollution in the fourier space representation of non-periodic signals over finite domains

Paulo L.K. Paes, Yuan Xuan, Yash G. Shah, James G. Brasseur

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

We present a strategy to remove the broadband Fourier spectral content associated with the boundary discontinuities in non-periodic directions of signals over finite domains, with negligible modification of the scales of interest in the original signal. The discontinuities arise from the signal decomposition using the Fourier harmonic basis functions that are defined over infinite domain, so the periodically extended signal in non-periodic directions includes a discontinuity at the boundaries between the signal and its periodic extension. The specific Fourier content associated with the non-periodicity of an arbitrary physical signal is identified and a procedure is developed to systemically isolate its spectral content with minimal modification of the original signal. The proposed “discontinuity pollution removal” procedure is first developed for C0 boundary discontinuities in one-dimensional signals, and then extended to higher order CN >0 boundary discontinuities in multi-dimensional signals with one non-periodic direction. This procedure allows for the analysis of signals over finite domains with the Fourier decomposition regardless of boundary conditions. We validate and demonstrate the capabilities of the proposed procedure for a test case of engineering relevance.

Original languageEnglish (US)
Title of host publicationAIAA Scitech 2019 Forum
PublisherAmerican Institute of Aeronautics and Astronautics Inc, AIAA
ISBN (Print)9781624105784
DOIs
StatePublished - Jan 1 2019
EventAIAA Scitech Forum, 2019 - San Diego, United States
Duration: Jan 7 2019Jan 11 2019

Publication series

NameAIAA Scitech 2019 Forum

Conference

ConferenceAIAA Scitech Forum, 2019
CountryUnited States
CitySan Diego
Period1/7/191/11/19

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering

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