6th International ICST Conference on Communications and Networking in China

Research Article

On the Linear Fractional Shift Invariant Systems Associated With Fractional Fourier Transform

  • @INPROCEEDINGS{10.1109/ChinaCom.2011.6158207,
        author={Jun Shi and Xuejun Sha and Xiaocheng Song and Naitong Zhang Zhang},
        title={On the Linear Fractional Shift Invariant Systems Associated With Fractional Fourier Transform},
        proceedings={6th International ICST Conference on Communications and Networking in China},
        publisher={IEEE},
        proceedings_a={CHINACOM},
        year={2012},
        month={3},
        keywords={fractional filtering distortionless transmission fractional fourier transform linear time invariant systems},
        doi={10.1109/ChinaCom.2011.6158207}
    }
    
  • Jun Shi
    Xuejun Sha
    Xiaocheng Song
    Naitong Zhang Zhang
    Year: 2012
    On the Linear Fractional Shift Invariant Systems Associated With Fractional Fourier Transform
    CHINACOM
    IEEE
    DOI: 10.1109/ChinaCom.2011.6158207
Jun Shi1, Xuejun Sha1, Xiaocheng Song1,*, Naitong Zhang Zhang1
  • 1: Harbin Institute of Technology
*Contact email: xcsonghit@yahoo.cn

Abstract

The fractional Fourier transform (FRFT) has been shown to be a powerful analyzing tool in signal processing. Many properties of this transform have been currently derived as counterparts to the corresponding properties of the Fourier transform (FT), including the theory of the linear fractional shift invariant (LFSI) systems. However, the LFSI systems, which are derived as extensions of the linear time invariant (LTI) systems, available in the literature do not generalize very nicely the LTI systems, which state that the output of a LTI system does not depend on the particular time the input is applied, and the FT of the output is the product of the transfer function and the FT of the input in the Fourier domain. In this paper, we propose a new LFSI system structure associated with the FRFT, and the LTI systems are noted as special cases. The eigenfunctions and eigenvalues of the new LFSI systems are presented. Moreover, the conditions for distortionless transmission in the fractional Fourier domain and basic properties of the ideal fractional filter are derived. Some applications of the achieved results are also discussed.