Frequency and damping factor estimation, i.e., modal signal analysis, is a very important technical topic [1] – [11] . The Prony method [3] is widely used for frequency and damping estimation [4] , [5] and is quite popular, although it suffers from poor noise immunity. In this article, we present a simple-to-implement trick, without any additional computational load, that improves the noise immunity of the Prony method. It is based on the proper selection of the sampling frequency [6] – [11] , which seems to be overlooked in the signal processing community, or application of polyphase decomposition [12] to already acquired oversampled signals [10] . It is explained that having approximately four samples for the signal cycle is beneficial since if the sampling frequency is approximately four times the signal frequency, then approximate diagonalization of the 2 $\times$ 2 signal autocorrelation matrix occurs for a single damped sinusoid, which further results in its robust inversion in the linear prediction (LP) solution.

中文翻译：

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多相 Prony 方法 [提示与技巧]

频率和阻尼因子估计，即模态信号分析，是一个非常重要的技术课题[1] – [11] . 普罗尼方法[3]广泛用于频率和阻尼估计[4] ,[5]并且很受欢迎，尽管它的抗噪能力很差。在本文中，我们介绍了一种易于实现的技巧，无需任何额外的计算负载，可提高 Prony 方法的抗噪性。它基于正确选择采样频率[6] – [11] ，这在信号处理界似乎被忽视了，或者多相分解的应用[12]到已经采集的过采样信号[10] . 解释说，对于信号周期有大约四个样本是有益的，因为如果采样频率大约是信号频率的四倍，那么 2 的近似对角化$\次$2 信号自相关矩阵出现在单个阻尼正弦曲线上，这进一步导致其在线性预测 (LP) 解决方案中的稳健反演。