Linear summation of fractional-Order matrices

Ran Tao; Feng Zhang; Yue Wang

doi:10.1109/TSP.2010.2044288

Linear summation of fractional-Order matrices

Ran Tao^*, Feng Zhang, Yue Wang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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 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.

Original language	English
Article number	5419993
Pages (from-to)	3912-3916
Number of pages	5
Journal	IEEE Transactions on Signal Processing
Volume	58
Issue number	7
DOIs	https://doi.org/10.1109/TSP.2010.2044288
Publication status	Published - Jul 2010

Keywords

Diagonalizable matrix
Discrete fractional Fourier transform
Eigendecomposition
Fractional-order matrix

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10.1109/TSP.2010.2044288

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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 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.",

keywords = "Diagonalizable matrix, Discrete fractional Fourier transform, Eigendecomposition, Fractional-order matrix",

author = "Ran Tao and Feng Zhang and Yue Wang",

year = "2010",

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language = "English",

volume = "58",

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T1 - Linear summation of fractional-Order matrices

AU - Tao, Ran

AU - Zhang, Feng

AU - Wang, Yue

PY - 2010/7

Y1 - 2010/7

N2 - 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.

AB - 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.

KW - Diagonalizable matrix

KW - Discrete fractional Fourier transform

KW - Eigendecomposition

KW - Fractional-order matrix

UR - http://www.scopus.com/inward/record.url?scp=77953768300&partnerID=8YFLogxK

U2 - 10.1109/TSP.2010.2044288

DO - 10.1109/TSP.2010.2044288

M3 - Article

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SN - 1053-587X

VL - 58

SP - 3912

EP - 3916

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

IS - 7

M1 - 5419993

ER -

Linear summation of fractional-Order matrices

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Keywords

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