Exact Fourier Spectrum Recovery

TL;DR

This paper introduces an exact Fourier spectrum recovery method that overcomes DFT limitations, providing an algorithm that accurately reconstructs frequencies outside the sampling grid and demonstrates robustness to noise.

Contribution

The paper presents a novel method and implementation for exact Fourier spectrum recovery, addressing DFT's inaccuracy with off-grid frequencies and noise robustness.

Findings

Method accurately recovers off-grid frequencies

Algorithm demonstrates robustness to noise

Outperforms traditional DFT in spectrum recovery

Abstract

Discrete Fourier Transform (DFT) is widely used in signal processing to analyze the frequencies in a discrete signal. However, DFT fails to recover the exact Fourier spectrum, when the signal contains frequencies that do not correspond to the sampling grid. Here, we present an exact Fourier spectrum recovery method and we provide an implementation algorithm. Also, we show numerically that the proposed method is robust to noise perturbations.