A perturbative analysis for noisy spectral estimation
<|reference_start|>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 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.<|reference_end|>
@article{ying2024a,
    title={A perturbative analysis for noisy spectral estimation},
    author={Lexing Ying},
    journal={arXiv preprint arXiv:2405.00803},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.00803},
    primaryClass={math.NA cs.NA}
}