离散分数阶Fourier变换的实现及有限字长效应分析

分数阶Fourier变换广泛的应用提出了在DSP上实现分数阶Fourier变换的需求。文章首先对离散分数阶Fourier变换算法的实现进行了改进,用额外的存储空间减少了运算量和误差。针对在定点DSP上的实现,对有限字长效应进行了理论分析,发现误差的方差随着计算点数线性增长,随着数据的存储字长呈指数下降。仿真结果表明了理论分析的正确性。

Implementation of discrete fractional Fourier transform and fixed-point error analysis

The fractional Fourier transform(FRFT) and its applications are introduced first,then the most typical algorithm of the discrete fractional Fourier transform(DFRFT) is described,and the implementation of the DFRFT on the fixed-point digital signal processor is studied. In order to save computation and also minimize the fixed-point errors,the algorithm is improved,and the effect of finite register length on implementation of the DFRFT matrix is discussed in detail. It is found that the variance of the error increases linearly with the number of points and decreases exponentially with the word-length of the digital signal processor(DSP). Simulation results show the correctness of the theoretical analysis.