Perturbation in the Fractional Fourier Span due to Erroneous Transform Order and Window Function
Fractional Fourier Transform is a generalization of the
classical Fourier Transform. The Fractional Fourier span in general
depends on the amplitude and phase functions of the signal and varies
with the transform order. However, with the development of the
Fractional Fourier filter banks, it is advantageous in some cases to
have different transform orders for different filter banks to achieve
better decorrelation of the windowed and overlapped time signal. We
present an expression that is useful for finding the perturbation in the
Fractional Fourier span due to the erroneous transform order and the
possible variation in the window shape and length. The expression is
based on the dependency of the time-Fractional Fourier span
Uncertainty on the amplitude and phase function of the signal. We
also show with the help of the developed expression that the
perturbation of span has a varying degree of sensitivity for varying
degree of transform order and the window coefficients.
[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] Tatiana Alieva and Martin J. Bastiaans, "On Fractional Fourier
Transform Moments", IEEE Signal Processing Letters, vol. 7, no. 11,
November 2000.
[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] Tatiana Alieva and Martin J. Bastiaans, "On Fractional Fourier
Transform Moments", IEEE Signal Processing Letters, vol. 7, no. 11,
November 2000.
@article{"International Journal of Electrical, Electronic and Communication Sciences:58422", author = "Sukrit Shankar and Chetana Shanta Patsa and Jaydev Sharma", title = "Perturbation in the Fractional Fourier Span due to Erroneous Transform Order and Window Function", abstract = "Fractional Fourier Transform is a generalization of the
classical Fourier Transform. The Fractional Fourier span in general
depends on the amplitude and phase functions of the signal and varies
with the transform order. However, with the development of the
Fractional Fourier filter banks, it is advantageous in some cases to
have different transform orders for different filter banks to achieve
better decorrelation of the windowed and overlapped time signal. We
present an expression that is useful for finding the perturbation in the
Fractional Fourier span due to the erroneous transform order and the
possible variation in the window shape and length. The expression is
based on the dependency of the time-Fractional Fourier span
Uncertainty on the amplitude and phase function of the signal. We
also show with the help of the developed expression that the
perturbation of span has a varying degree of sensitivity for varying
degree of transform order and the window coefficients.", keywords = "Fractional Fourier Transform, Perturbation,Fractional Fourier span, amplitude, phase, transform order, filterbanks.", volume = "2", number = "1", pages = "124-3", }