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.

翻译：谱估计是信号处理中的基本任务。近年来量子相位估计算法关注谱估计问题中的大噪声、大频率区域。Ding-Epperly-Lin-Zhang的最新研究表明，ESPRIT算法对尖峰位置的最大频率项展现出超收敛特性。本文通过微扰分析解释了这一现象，并将讨论推广至噪声随采样频率增长的情形。