Linear summation of fractional-order matrices

Authors:
Ran Tao;Feng Zhang;Yue Wang
Affiliations:
Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China;Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China;Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China
Venue:
IEEE Transactions on Signal Processing
Year:
2010

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Abstract

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 fractionalorder 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.