分数阶S变换：第一部分，理论

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摘要 S变换(ST)结合了小波变换和短时傅里叶变换的特性，对信号处理具有良好的局部时频聚集性.分数阶傅里叶变换是一种对非平稳信号分析的工具.本文基于分数阶傅里叶变换和S变换的思想，提出了分数阶S变换（FRST），将S变换从时间-频率域推广到时间-分数阶频率域，推导了它的逆变换公式并研究了其数学性质。分数阶S变换（FRST）具有分数阶傅里叶变换和S变换的优点，增强了S变换对信号处理的灵活性。相比于S变换，分数阶S变换能提高信号时频分辨能力。仿真实验证实了该方法的有效性。

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	胥德平
	郭科

关键词：分数阶S变换分数阶傅里叶变换分数阶时频分析

Abstract： The S transform, which is a time-frequency representation known for its local spectral phase properties in signal processing, uniquely combines elements of wavelet transforms and the short-time Fourier transform (STFT). The fractional Fourier transform is a tool for non-stationary signal analysis. In this paper, we defi ne the concept of the fractional S transform (FRST) of a signal, based on the idea of the fractional Fourier transform (FRFT) and S transform (ST), extend the S transform to the time-fractional frequency domain from the timefrequency domain to obtain the inverse transform, and study the FRST mathematical properties. The FRST, which has the advantages of FRFT and ST, can enhance the ST fl exibility to process signals. Compared to the S transform, the FRST can effectively improve the signal timefrequency resolution capacity. Simulation results show that the proposed method is effective.

Key words： fractional S transform fractional Fourier transform time-frequency analysis

收稿日期: 2011-12-30;

基金资助:

本研究项目由国家自然科学基金项目（No. 40873035），中国地质调查局项目（No. 1212010916040）和四川省教育厅资助科研项目支持。

引用本文:

胥德平,郭科. 分数阶S变换：第一部分，理论[J]. 应用地球物理, 2012, 9(1): 73-79.

XU De-Ping,GUO Ke. Fractional S transform – Part 1: Theory*[J]. APPLIED GEOPHYSICS, 2012, 9(1): 73-79.

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