Exact bounds on the amplitude and phase of the interval discrete Fourier transform in polynomial time

Research output: Working paper

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Abstract

We elucidate why an interval algorithm that computes the exact bounds on the amplitude and phase of the discrete Fourier transform can run in polynomial time. We address this question from a formal perspective to provide the mathematical foundations underpinning such an algorithm. We show that the procedure set out by the algorithm fully addresses the dependency problem of interval arithmetic, making it usable in a variety of applications involving the discrete Fourier transform. For example when analysing signals with poor precision, signals with missing data, and for automatic error propagation and verified computations.
Original languageEnglish
Place of PublicationIthaca, NY
Number of pages17
DOIs
Publication statusPublished - 27 May 2022

Keywords

  • signal processing
  • reliable computing
  • Fourier transform

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