特征分解型离散分数阶Fourier变换

Discrete Fractional Fourier Transform Algorithm Based on New Eigendcomposition Algorithm

分数阶Fourier变换作为Fourier变换的广义形式,广泛应用于科学计算和研究,离散分数阶Fourier变换是其得以应用的关键。特征分解算法是由可交换对角矩阵得到近似连续Hermite-Gaussian函数的特征向量,再对Hermite-Gaussian函数进行加权和运算。对一种基于数特征分解的方法进行了改进,并进行计算机仿真。仿真结果表明所得的Hermite-Gaussian函数与连续函数的近似度更为优异,从而提高了离散分数阶Fourier变换的近似度。

Fractional Fourier transform （FRFT） as a Fourier transform of the generalized form is widely used in scientific computing and engineering research,and discrete Fourier transform（DFRFT） algorithm is the key for application. Eigendcomposition algorithm is based on the tridiagonal commuting matrix which provides sample approximations of the continuous Hermite-Gaussian like functions,and the DFRFT is interpreted as a weighting summation of Hermite-Ganssian functions. An improved algorithm is simulated. The simulation results show that the obtained Hermite-Ganssian function and continuous function approximation degree more excellent, so as to increase the discrete Fourier transform fractional order approximate degrees.