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

Tools

de Angelis, M. (2022) Exact bounds on the amplitude and phase of the interval discrete Fourier transform in polynomial time. Preprint / Working Paper. arXiv, Ithaca, NY. (https://doi.org/10.48550/arXiv.2205.13978)

[thumbnail of de-Angelis-ArXiv-2022-Exact-bounds-on-the-amplitude-and-phase]
Preview
 Text. Filename: de_Angelis_ArXiv_2022_Exact_bounds_on_the_amplitude_and_phase.pdf
Final Published Version
License: Creative Commons Attribution 4.0 logo
Download (719kB)| Preview

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.

ORCID iDs

de Angelis, M. ORCID logoORCID: https://orcid.org/0000-0001-8851-023X;
CORE (COnnecting REpositories)