A perturbative analysis for noisy spectral estimation
Numerical Analysis
2024-05-03 v1 Numerical Analysis
Abstract
Spectral estimation is a fundamental task in signal processing. Recent algorithms in quantum phase estimation are concerned with the large noise, large frequency regime of the spectral estimation problem. The recent work in Ding-Epperly-Lin-Zhang shows that the ESPRIT algorithm exhibits superconvergence behavior for the spike locations in terms of the maximum frequency. This note provides a perturbative analysis to explain this behavior. It also extends the discussion to the case where the noise grows with the sampling frequency.
Keywords
Cite
@article{arxiv.2405.00803,
title = {A perturbative analysis for noisy spectral estimation},
author = {Lexing Ying},
journal= {arXiv preprint arXiv:2405.00803},
year = {2024}
}