S变换与小波变换检测信号突变性研究

Research on detecting abrupt changes of signals via S transform and wavelet transform

时间局部谱分析方法的研究对信号突变性检测具有重要意义。S变换是加窗傅里叶变换和连续小波变换思想的延伸或推广,S变换保持了与傅里叶谱的直接联系,提供了依赖于频率的分辨率,具有连续小波变换所没有的一些特点。介绍了S变换和广义S变换的数学原理,分析了S变换与加窗傅里叶变换和小波变换之间的关系,对一个突变信号在S变换与小波变换下的表现特征进行研究,结果表明,S变换能比小波变换更直观更清楚地表现信号突变位置。

Study on time-local spectrum analysis methods has great significance for detecting abrupt changes in signals. S transform is an extension of the ideas of the windowed Fourier transform and continuous wavelet transform. Maintaining a direct relationship with the Fourier spectrum, providing frequency-dependent resolution, S transform have some desirable characteristics that are absent in the continuous wavelet transform. Based on the analyses for S transform as well as its relations with the Gabor transform and wavelet transform, abrupt change features in signals are explored. The results show that S transform can more intuitively and effectively demonstrates sudden change locations in signals than the wavelet transform.