傅立叶变换性质在瞬时频率构造中的应用

The application of the properties of Fourier transform in instantaneous frequency structure

利用傅立叶变换的性质研究信号希尔伯特变换的频谱特征。在频域内一个因果信号的频谱实部与虚部互为变换。一个信号和它的变换式能构成一个解析信号,解析信号的实部就是原信号,其虚部是原信号的希尔伯特变换;解析信号的傅立叶频谱只有正频率部分,正好是原信号正频率部分的二倍,并且该解析信号的幅值和相位就表征了原信号的幅值包络和瞬时频率变化特征,这样就使瞬时频率瞬时幅值有了明确的物理意义,对研究非线性非稳态信号有非常重要的价值。

This paper studies spectrum characteristics of the Hilbert transformation bythe properties of the Fourier transformation. In frequency domain,real part and imaginary part of a causal signal spectrum are the Hilbert transformation each other. A signal and its Hilbert transform can constitute a analytical signal,the real partof the analytical signal is the original signal,the imaginary part is the Hilbert transformation of the original signal; The Fourier spectrum of analytical signal contains only the positive frequencypart,which isjust two times of the original signal,and the analytic signal amplitude and phase will represent the original signal amplitude envelope and instantaneous frequency variation characteristics,so the instantaneous frequency and instantaneous amplitude have clear physical meaning,which is very important to study nonlinear unsteady signal.