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An Efficient Hamiltonian for Discrete Fractional Fourier Transform

Authors: Sukrit Shankar, Pardha Saradhi K., Chetana Shanta Patsa, Jaydev Sharma


Fractional Fourier Transform, which is a generalization of the classical Fourier Transform, is a powerful tool for the analysis of transient signals. The discrete Fractional Fourier Transform Hamiltonians have been proposed in the past with varying degrees of correlation between their eigenvectors and Hermite Gaussian functions. In this paper, we propose a new Hamiltonian for the discrete Fractional Fourier Transform and show that the eigenvectors of the proposed matrix has a higher degree of correlation with the Hermite Gaussian functions. Also, the proposed matrix is shown to give better Fractional Fourier responses with various transform orders for different signals.

Keywords: Fractional Fourier Transform, Hamiltonian, Eigen Vectors, Discrete Hermite Gaussians.

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[1] S. C. Pei and M. H. Yeh, "Improved discrete fractional Fourier transform," Optics Letters, vol. 22, pp. 1047-1049, July 15 1997.
[2] Ahmed I. Zayed, "Relationship between the Fourier and Fractional Fourier Transforms", IEEE Signal Processing Letters, vol. 3, no. 12, December 1996.
[3] C. Candan, M.A. Kutay, H.M. Ozaktas, "The Discrete Fractional Fourier Transform", O-7803-5041-3, !EEE 1999.
[4] S.C. Pei and M.H. Yeh, "Discrete Fractional Fourier Transform", O- 7803-3073/0, IEEE 1996.