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 proves that the ESPRIT algorithm exhibits superconvergence behavior for the spike locations in terms of the maximum frequency. This note provides a perturbative analysis to understand this behavior and extends to the case where the noise grows with the sampling frequency. However, this does not imply or explain the rigorous error bound obtained by Ding-Epperly-Lin-Zhang.

中文翻译：

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用于噪声频谱估计的扰动分析


频谱估计是信号处理中的一项基本任务。最近的量子相位估计算法关注的是频谱估计问题的大噪声、大频率状态。Ding-Epperly-Lin-Zhang 最近的工作证明，ESPRIT 算法在最大频率方面表现出尖峰位置的超收敛行为。本说明提供了扰动分析来理解这种行为，并扩展到噪声随采样频率增加的情况。但是，这并不意味着或解释 Ding-Epperly-Lin-Zhang 获得的严格误差边界。