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小波变换是被广泛使用的信号时频分析的有效工具,但小波变换时频谱的分辨率达不到最优.最近提出的同步挤压变换以严格的数学推导为基础,通过对小波变换结果进行“挤压”和重排,能够获得更高分辨率的时频谱.由于小波变换难以较好地反映信号中的高频低振幅分量,使得基于小波变换的同步挤压变换也很难反映信号中的高频低振幅分量.相比之下,S变换能够较好地刻画信号中的高频低振幅分量,并能实现无损逆变换,但与小波变换一样,它的时频谱分辨率也达不到最优.为了提高S变换的分辨率,本文提出了同步挤压S变换,给出了同步挤压S变换的基本理论,推导出了同步挤压S变换及其逆变换的数学表达式.分别使用小波变换、S变换、同步挤压变换和同步挤压S变换对理论合成信号进行处理.结果表明,同步挤压S变换兼顾了S变换和同步挤压变换的优势,不仅能够极大地提高信号时频变换的分辨率,而且能够较好地反映信号中弱振幅分量的时频特征.
Wavelet transform is widely used as an effective tool for time-frequency analysis of signals, but the resolution of the spectrum is not optimal when wavelet transform is adopted.Recently proposed synchronous squeezing transform is based on rigorous mathematical derivation, “Squeeze ” and rearrangement, can get a higher resolution time-frequency spectrum.Wavelet transform is difficult to reflect the high-frequency low amplitude components of the signal, so that the wavelet transform based on the synchronous squeeze transform is difficult to reflect In contrast, the S transform can better characterize the high-frequency and low-amplitude components of the signal, and can achieve lossless inverse transform, but as with wavelet transform, its time-frequency resolution In order to improve the resolution of S transform, this paper presents synchronous squeezing S transform, gives the basic theory of synchronous squeezing S transform, and deduces the mathematical expression of synchronous squeeze S transform and its inverse transform The theoretical synthesis signals are processed by wavelet transform, S transform, synchronous squeeze transform and synchronous squeeze S transform, respectively.The results show that the synchronous squeeze S transform takes into account the advantages of S transform and synchronous squeeze transform, The resolution of the frequency transformation signals increase, but can reflect a weak signal amplitude component frequency characteristic.