过采样下分数阶傅里叶变换的改进算法

摘要

针对Ozaktas采样型分数阶傅里叶变换(fractional Fourier transform,FRFT)的计算量偏大以及分辨率较低的弱点,研究了过采样条件下采样型FRFT的计算,提出了一种改进算法.在过采样条件下,通过减小变换阶的取值范围,使在时频平面上的频率分布范围缩小,时域离散间隔保持不变,避免了插值运算,计算量明显减小,且算法具有可逆性.经过进一步拓展,改进算法具有分辨率可调,输出区域可选,输出长度可变的特点.最后通过数值仿真对改进算法进行了验证.%For the weakness that Ozaktas sampling-type fractional Fourier transform (FRFT) has high computational complexity and low resolution, the computation of sampling-type FRFT is investigated under a condition of over-sampling, and an improved algorithm of FRFT is presented. By reducing the value range of FRFT under the condition of oversampling,the frequency distribution in time-frequency plane is decreased and the discrete interval keeps the same as samples in time domain. Therefore, the interpolation is avoided and the computation is simplified significantly in the improved algorithm. Moreover, the improved algorithm is invertible. After further improvement, the algorithm has features with adjustable resolution, selectable output region and variable length of output data. The simulation results show the validity of the improved algorithm finally.