瞬时频率计算方法的比较研究和改进

Comparative research and improvement on the calculation method of instantaneous frequency

希尔伯特-黄变换是目前最广泛使用的提取信号瞬时频率时频分析方法,但在求取瞬时频率过程存在端点效应问题.针对这个问题,本文从解析信号的瞬时频率定义着手,介绍了Bedrosian等式和Nuttall定理的限制条件,分析了希尔伯特变换端点效应的产生原因,研究了基于经验调幅调频分解求取瞬时频率的方法及原理.在此基础上比较了希尔伯特变换、Teager能量算子和直接正交法在求取瞬时频率的优缺点.通过实例验证可以得出以下结论:(1)希尔伯特变换解调信号端点效应明显;(2)Teager能量算子法易受信号形式和噪声影响,误差较大;(3)直接正交法易受信号极值点影响,在极值点处会产生瞬时频率突变.针对直接正交法存在的问题,提出了一种改进算法,仿真结果表明:改进算法的效果较为理想,误差较小,能够解决直接正交法求取瞬时频率在极值点处发生突变的问题.

Hilbert-Huang Transform is currently a time-frequency analysis method which is the most widely used to extract instantaneous frequency of the signals, but there is the problem of end effect in the process of obtaining instantaneous frequency. Aiming at this problem, the limited conditions of Bed- rosian identity and Nuttall theorem are introduced by means of the definition of instantaneous frequency of analytic signal, and the causes of end effect of Hilbert transform are analyzed, and then the methods and principles of calculating instantaneous frequency are studied based on empirical AM-FM decomposi- tion. On this basis, the advantages and disadvantages of obtaining instantaneous frequency by means of the three methods are in comparison with Hilbert transform method, Teager energy operator method and direct quadrature method. And The following conclusions can be made by verified examples： firstly, the phenomenon of end effect by Hilbert transform is obvious; secondly, Teager energy operator method is easy to susceptible to signal form and noise, and the error is relatively large; thirdly, direct quadra- ture method can be influenced by signal extreme points and brings in the mutations of instantaneous fre- quency. For the problem of direct quadrature method, an improved algorithm is proposed, and it can be shown that from the simulation results： the improved algorithm is more satisfactory, the error is smal-ler, and the mutation on the extreme points of instantaneous frequency can be solved by the improved di- rect quadrature method.