The Bi-Gaussian S-Transform
The Bi-Gaussian S-Transform
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DOI：
10.1137/s1064827500369803
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发表时间：
2002-05
期刊：
影响因子：
--
通讯作者：
C. Pinnegar;L. Mansinha
中科院分区：
文献类型：
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作者：
C. Pinnegar;L. Mansinha
S变换核是通过引入可缩放的平移窗口从傅立叶变换的核导出的。窗口的宽度是频率倒数的函数。实际上，S变换是一种谱局部化的方法，与小波变换有一些相似之处，但使用频率的概念而不是尺度的概念。S变换的一个重要性质是，当在时间轴上积分时，它会塌陷到傅立叶变换中;这个性质要求窗口满足归一化条件。在大多数先前的S变换研究中已经使用的窗口是由Stockwell、Mansinha和Lowe [IEEE Trans. Signal Process.，44（1996），第44页。998- 1001]。然而，使用高斯的一个问题是由于长的前锥而导致的时间-频谱中的时间分辨率的退化。本文介绍了一种双高斯窗，它是由两个半高斯窗焊接而成。双高斯的不对称性在所得到的时间-频谱中引入了不对称性，与“后”方向相比，“前”方向的时间分辨率更好。双高斯S变换在解决时间序列中事件的尖锐开始方面更好。
The S-transform kernel is derived from the kernel of the Fourier transform through the introduction of a scalable, translating window. The width of the window is a function of inverse frequency. In effect the S-transform is a method of spectral localization, with some similarities to wavelet transforms but using the concept of frequency rather than the concept of scale. An important property of the S-transform is that it collapses into the Fourier transform when integrated over the time axis; this property requires the window to satisfy a normalizing condition. The window which has been used in the majority of previous S-transform research is the symmetric Gaussian window introduced by Stockwell, Mansinha, and Lowe [IEEE Trans. Signal Process., 44 (1996), pp. 998--1001]. One problem with the use of a Gaussian, however, is degradation of time resolution in the time-frequency spectrum due to the long front taper. In this paper, a bi-Gaussian window is introduced, constructed through the welding of two half Gaussian windows. The asymmetry of the bi-Gaussian introduces asymmetry in the resultant time-frequency spectrum, with time resolution better in the "front" direction, as compared with the "back" direction. The bi-Gaussian S-transform is better at resolving the sharp onset of events in a time series.