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



Angelis, Marco de
(2022) Exact bounds on the amplitude and phase of the interval discrete Fourier transform in polynomial time. [Preprint]

[img] Text
de Angelis - 2022 - Exact bounds on the amplitude and phase of the int.pdf - Submitted version

Download (184kB) | 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.

Item Type: Preprint
Additional Information: Manuscript submitted to the journal of Reliable Computing on 17 December 2021
Uncontrolled Keywords: math.NA, math.NA, cs.NA, cs.SY, eess.SP, eess.SY
Depositing User: Symplectic Admin
Date Deposited: 27 Oct 2022 16:33
Last Modified: 18 Jan 2023 19:49
DOI: 10.48550/arXiv.2205.13978
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3165656