基于短时分数阶傅里叶变换的时频分析方法

Time-Frequency Analysis Method Based on Short-Time Fractional Fourier Transform

本文研究了短时分数阶傅里叶变换(STFRFT)时频分析方法的分辨率精度和算法性能.首先,文中给出了一种STFRFT时频分辨率的数学计算表达式,其有利于时频分辨率的量化比较,仿真结果表明该理论量化值与观察值基本吻合;其次,针对算法运算量大的问题,提出了一种STFRFT的快速计算方法,它较传统的穷举搜索方法运算量约降低1个数量级;最后,给出了算法估计误差的理论分析并运用该方法对多目标信号进行了分析,仿真表明该方法可有效抑制交叉项和解决多分量时频信号的分离问题.

The resolution precision and algorithm stability of the short-time fractional Fourier transform （STFRFT） time-fre-quency method was studied .Firstly ,the mathematical expression of the STFRFT time-frequency resolution was given in this paper , which is beneficial to the time-frequency resolution theory quantitative comparison ,and simulation results showed that the theoretical quantitative value is basically consistent with the observed value .Secondly ,this paper proposed a fast calculation method of STFRFT to decrease the computational complexity ,its calculation amount comparing with the traditional search method was reduced about an order of magnitude ;Finally ,the paper gave the estimation error theoretical analysis of the algorithm and applied the method to ana-lyze the multi-target signal .The simulation results showed that this method could effectively suppress cross-terms and resolve the problem of multi-component signal separation .