A perturbative analysis for noisy spectral estimation

TL;DR

This paper provides a perturbative analysis to explain the superconvergence behavior of the ESPRIT spectral estimation algorithm, especially under large noise and high frequency regimes, extending understanding of its robustness.

Contribution

It introduces a perturbative framework to analyze ESPRIT's superconvergence and extends the analysis to scenarios with noise increasing with sampling frequency.

Findings

ESPRIT exhibits superconvergence for spike locations.

The analysis explains robustness under large noise.

Extension to noise growing with sampling frequency.

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.