An Efficient Hamiltonian for Discrete Fractional Fourier Transform
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.
[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.
[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.
@article{"International Journal of Electrical, Electronic and Communication Sciences:59350", author = "Sukrit Shankar and Pardha Saradhi K. and Chetana Shanta Patsa and Jaydev Sharma", title = "An Efficient Hamiltonian for Discrete Fractional Fourier Transform", abstract = "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.", volume = "2", number = "7", pages = "1480-6", }