噪声频谱估计的扰动分析

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2024-10-18 DOI:10.1016/j.acha.2024.101716

Lexing Ying

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引用次数: 0

摘要

频谱估计是信号处理中的一项基本任务。量子相位估计的最新算法关注的是频谱估计问题的大噪声、大频率机制。Ding-Epperly-Lin-Zhang 的最新研究证明，ESPRIT 算法在尖峰位置的最大频率方面表现出超收敛行为。本论文提供了一种扰动分析来理解这种行为，并扩展到噪声随采样频率增长的情况。然而，这并不意味着或解释丁-埃珀利-林-张所获得的严格误差约束。

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A perturbative analysis for noisy spectral estimation

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.

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来源期刊

Applied and Computational Harmonic Analysis 物理-物理：数学物理

CiteScore

5.40

自引率

4.00%

发文量

审稿时长

22.9 weeks

期刊介绍： Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.