奇异值分析与多项式拟合解调在调频信号处理中的应用
Application of Singular Value Analysis and Polynomial Fitting Demodulation in Frequency Modulated Signal Processing

为了解决传统方法对调频信号处理效果不佳问题，基于奇异值提出一种新方法。利用Hankel矩阵研究常见信号奇异值突变特征，分析相关奇异值与信号具体特征的对应关系，为重构信号所需有效奇异值提供选择依据。针对调频信号奇异值突变特征不明显问题，根据Weierstrass逼近定理采用多项式拟合描述调频信号的调频规律；提出最小奇异值分布差准则，以实现信号瞬时频率函数参量确定的最优估计；构造解调算子，解调得到具有明显奇异值突变特征的解调信号；引入调制源完成调频信号重构。通过仿真信号与航空发动机实测信号分析，表明多项式拟合解调与奇异值分解对调频信号降噪、分量提取具有很好的效果。
In order to solve the problem that traditional methods have poor performance to analyze frequency modulated (FM) signal, a new method based on singular value analysis is proposed. the singular value mutation characteristics of common signal is studied based on Hankel matrix and the correspondence relationship between the relevant singular value and the specific characteristics of signal is analyzed to provide the selection basis of effective singular value for signal reconstruction. Considering the problem that singular value mutation characteristics of the FM signal is not obvious, polynomial fitting is used to describe frequency modulation regularity of the FM signal according to the Weierstrass approximation theorem.; the minimum singular value distribution difference criterion is proposed to achieve the optimal estimation of the parameters of signal instantaneous frequency function; Then, signal demodulation is accomplished with the use of the established demodulation operator and its singular value owns obvious mutation characteristics; Finally, the FM signal is restructured by demodulation signal and modulation term. Analysis of simulation signal and actual measurement of aircraft engines shows the method of polynomial fitting demodulation and singular value decomposition (SVD) is effective for FM signal noise reduction and component extraction