基于FFT和DTFT的指数衰减复正弦信号参数估计算法

PARAMETER ESTIMATION ALGORITHM OF EXPONENTIALLY DECAYING COMPLEX SINUSOIDAL SIGNAL BASED ON FFT AND DTFT

针对加性高斯白噪声环境中指数衰减复正弦信号频率和衰减因子的估计问题,提出一种结合FFT和DTFT的离散三谱线插值算法。在利用FFT进行频率粗估计基础上,再利用FFT幅度最大谱线及其左右两侧任意相等位置处的DTFT辅助谱线进行频率和衰减因子精估计,并通过迭代提高算法性能。仿真结果表明,当辅助谱线距离幅度最大谱线位置的绝对值小于0.5时,信号实际频率位于FFT两条谱线之间任意位置,算法性能均接近克拉美罗下界,参数估计精度高于同类算法。

In order to estimate the frequency and the decaying factor of the exponentially decaying complex sinusoidal signal,we propose a discrete three spectral lines interpolation algorithm based on FFT and DTFT.After the rough estimation of frequency by FFT,the fine estimation of frequency and damping factor was made by utilizing the FFT spectrum line with maximum amplitude and two auxiliary spectral lines of the DTFT of the signal at any positions symmetrically located on the two sides of the maximum spectrum line.The performance of the algorithm was improved by iteration.The simulation results show that when the absolute value of the difference between discrete frequency index values of two auxiliary lines and the maximum spectral line is less than 0.5,the actual frequency of the signal is located in any position between the two FFT spectral lines,the performance of the algorithm is close to the Cramer-Rao lower bound,and the parameter estimation accuracy is higher than the similar algorithms.