加性噪声中未知分量数的谐波恢复方法研究
Research on Harmonic Retrieval Method in Additive Noise without Components Number

DOI: 10.12677/OE.2020.102005, PP. 38-45

Keywords: 谐波恢复，加性噪声，MUSIC算法，谐波分量数
Harmonic Retrieval, Additive Noise, MUSIC Algorithm, Number of Harmonic Components

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Abstract:

谐波恢复问题是信号处理中的经典问题，对于被加性噪声污染的谐波信号，现有的多重信号分类(MUSIC)方法可以实现良好的恢复效果，但在谐波分量数未知的情况下无法发挥其超分辨率性能。本文结合实值MUSIC算法的超分辨率和逐步LSE算法的逐步估计的特点，提出了一种逐步MUSIC算法，该算法在分量数已知的情况下具有良好的估计性能。在分量数未知的情况下，我们利用该算法估计出一个模型集，并采用BIC准则估计谐波分量数。最后通过仿真实验对所提方法的性能进行了验证。
The retrieval of harmonic signal is a classic problem in signal processing. Consider harmonic signals in additive noise, among the proposed schemes in related literatures, the MUSIC (Multiple Signal Classification) algorithm can achieve good retrieval performance. However, it can’t play its super-resolution performance when the number of harmonic components is unknown. In this paper, we combine the super-resolution of real-value MUSIC algorithm and the step-by-step estimation of step-by-step LSE algorithm, a step-by-step MUSIC algorithm is proposed. Our algorithm has good estimation performance when the number of components is known. When the number of components is unknown, we use the algorithm to estimate a model set, and estimate the number of harmonic components with the Bayesian Information Criterion (BIC). Finally, the performance of the proposed method is verified by simulation experiments.

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