希尔伯特-黄变换中边际谱的研究

为了深入理解和正确掌握希尔伯特 黄变换(Hilbert HuangTransform,简称HHT)中的边际谱概念,证明了边际谱的线性性质,指出了文献中对边际谱概念的一种误解,提出了边际普与Fourier频谱之间本质区别的一种的新观点,即Fourier频谱的幅值只能反映频率在信号中实际存在的可能性大小,而边际谱的幅值则能真实反映频率在信号中是否存在。利用边际谱的线性性质进一步给出了边际谱的物理意义,即边际谱的幅值表示信号中某一频率在各个时刻的幅值之和。通过一个实测振动信号验证了边际谱在应用中的优越性。

Study on the marginal spectrum in Hilbert-Huang transform

To further understand and correctly master the notion of marginal spectrum in Hibert-huang Transform (HHT), the linear property of marginal spectrum is demonstrated, an mistake to the notion of marginal spectrum in some documents is pointed out, and a new viewpoint about the essential difference between marginal spectrum and Fourier frequency spectrum is put forward by which the amplitude of Fourier frequency spectrum only represents the probability that a frequency objectively exists in a signal while the amplitude of marginal spectrum decides whether a frequency objectively exists in a signal. According to the linear property of marginal spectrum, the physical meaning of marginal spectrum is further given by which a amplitude of marginal spectrum is the sum of amplitudes of the corresponding frequency at all time. The advantage of marginal spectrum in application is validated by an actual vibration signal.