采用频域Prony方法估计信号重叠双分量

Prony's method on frequency domain to estimate two overlapped components

给定加窗信号DFT峰值附近的5个点,应用汉宁窗的DTFT的性质,将表达式复杂的频率估计问题转化为简单的二元高次方程组,利用Prony方法将其进一步转化为差分方程的系数估计问题.将差分方程写成矩阵形式,利用数据矩阵的奇异值分解,得到判断插值点上重叠分量数目的方法、估计单分量和双分量的复频率的算法以及重叠分量数不小于3时的处理方法.在分量的复频率已知的情况下,分量的幅值和相位可以通过最小二乘法获得.当插值点仅包含单分量时,频域Prony方法和其他2种算法的估计误差十分接近;当插值点包含重叠双分量时,频域Prony方法能够同时得到2个分量的估计,但是其他2种算法失效.

Given five points around the peak of the windowed DFT values and based on the property of Hann window＇s DTFT,the estimation of complex frequencies was transformed to an equation group of higher degree with two unknowns.Solving the equation group was equivalent to estimating the coefficients of a difference equation according to Prony＇s method,The singular value decomposition method was applied by rewriting the difference equation into the matrix form,and the number of overlapped components on the interpolation points was evaluated.The algorithm to estimate single or double components was provided and easily extended to deal with three or more overlapped components.The amplitude and phase of components could be archived by the least squares method with frequencies estimated.When interpolation points contain only one component,all three methods have similar estimation results.when interpolation points contain two overlapped components,the proposed method provides accurate estimations,while the other two fail.