The discrete fractional Fourier transform and its simulation

In this paper, the definition, corresponding algorithm and the numerical simulation of the discrete fractional Fourier transform are studied. In the description of matrix, the classical discrete Fourier transform operator corresponds to a 4 x 4 cyclic matrix group; the discrete fractional Fourier transform operator corresponds to a 4 x 4 generalized permutation matrix; the operator group constituted by all the general discrete Fourier transforms can be described as a 4 x 4 generalized permutation matrix group, thus the variable multi-exponent transforms operator is converted to a corresponding matrix multiplication operator completely At the end of this paper, the discrete fractional Fourier transform simulation of the numerical signals corresponding to some common signals is realized with the discrete algorithms. The results show that the discrete fractional Fourier transform algorithm, which is proposed in this paper, is efficient. This algorithm provides much more choices than the discrete Fourier transform.