基于分数阶傅立叶变换的自适应时频表示

摘要

We propose a method of adaptive signal expansion based on fractional Fourier transform (FRFT) of Gaussian functions as the elementary functions and the related adaptive time-frequency distribution that is of better time-frequency resolution, free of window effect and cross-term interference. Fractional Fourier transform rotates the time-frequency distribution of the elementary functions, which will make the match between the signal and elementary functions more flexible in combination with scaling, time-shift and frequency-shift. Simulation results show that the method provides more precise representation of signal's time-frequency behavior.%提出采用高斯函数的分数阶傅立叶变换作为基函数的自适应信号扩展方法，并给出了相应的时频分布，该分布具有较高的时频分辨率，没有窗效应，无交叉项干扰。分数阶傅立叶变换使基函数的时频分布旋转了α角度，结合尺度，时移和频移，为基函数匹配信号提供了更大的灵活性。仿真结果表明，该方法可以更加准确地描述信号的时频特征。