快速提取正弦信号频率

本文在正弦信号频率估计的线性预测方法基础上,充分利用正弦信号的特殊性信息,给出了一种正弦信号频率估计的快速算法。文中首先利用线性预测参数的对称性将原线性预测方程的阶数降低一半求解,使其计算量减少到原来的八分之一。提取正弦信号的频率,还要求解一高次特征多项式方程,利用其系数的对称性,经过巧妙的根的变换,还可把该高次复根多项式方程的求解转化为次数减半的实根多项式方程的求解。该实根多项式方程的求解可此原复根多项式方程求解的速度提高八倍。文中最后给出计算机模拟结果,并与原线性预测方法和前后向线性预测方法加以此较。

A FAST ALGORITHM FOR SINUSOIDAL SIGNAL FREQUENCY ESTIMATION

In this paper, an approuch for fast multiple sinusoidal frequency estimation is proposed which is based on the commonly used linear prediction (LP) method. In this approuch, we first reduce the order of the LP equation to half of its original value by taking into account the information that all the poles of the siunsoidal components lie on the unit circle of the Z-plane. The LP parameters can be recursively computed and the number of siunsoidal components in the signal can also be determined simultaneously. To extract signal frequencies, a high order polynomial equation must be solved. An elegent transformation of its roots is performed so that the problem of solving this high order complex-root polynomial equation is converted to a problem of solving a real -root polynomial equation with its order reduced by a half. The roots of this new polynomial euqation not noly lie on the real axis, but also distribute in a known finite interval. Based on this property, a fast convergent algorithm is presented for finding the roots of this new polynomial equation. Finally, computer simulation results are given, and comparison with LP and FBLP methods is also made.