Linear Summation of Fractional-Order Matrices

Yeh and Pei presented a computation method for the discrete fractional Fourier transform (DFRFT) that the DFRFT of any order can be computed by a linear summation of DFRFTs with special orders. Based on their work, we investigate linear summation of fractional-order matrices in a general and comprehensive manner in this paper. We have found that for any diagonalizable periodic matrices, linear summation of fractional-order forms with special orders is related to the size and the period of the fractional-order matrix. Moreover, some properties and generalized results about linear summation of fractional-order matrices are also presented.