Quality Factor Variation with Transform Order in Fractional Fourier Domain
Fractional Fourier Transform is a powerful tool,
which is a generalization of the classical Fourier Transform. This
paper provides a mathematical relation relating the span in Fractional
Fourier domain with the amplitude and phase functions of the signal,
which is further used to study the variation of quality factor with
different values of the transform order. It is seen that with the
increase in the number of transients in the signal, the deviation of
average Fractional Fourier span from the frequency bandwidth
increases. Also, with the increase in the transient nature of the signal,
the optimum value of transform order can be estimated based on the
quality factor variation, and this value is found to be very close to
that for which one can obtain the most compact representation. With
the entire mathematical analysis and experimentation, we consolidate
the fact that Fractional Fourier Transform gives more optimal
representations for a number of transform orders than Fourier
transform.
[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 Information, Control and Computer Sciences:58554", author = "Sukrit Shankar and Chetana Shanta Patsa and K. Pardha Saradhi and Jaydev Sharma", title = "Quality Factor Variation with Transform Order in Fractional Fourier Domain", abstract = "Fractional Fourier Transform is a powerful tool,
which is a generalization of the classical Fourier Transform. This
paper provides a mathematical relation relating the span in Fractional
Fourier domain with the amplitude and phase functions of the signal,
which is further used to study the variation of quality factor with
different values of the transform order. It is seen that with the
increase in the number of transients in the signal, the deviation of
average Fractional Fourier span from the frequency bandwidth
increases. Also, with the increase in the transient nature of the signal,
the optimum value of transform order can be estimated based on the
quality factor variation, and this value is found to be very close to
that for which one can obtain the most compact representation. With
the entire mathematical analysis and experimentation, we consolidate
the fact that Fractional Fourier Transform gives more optimal
representations for a number of transform orders than Fourier
transform.", keywords = "Fractional Fourier Transform, Quality Factor,
Fractional Fourier span, transient signals.", volume = "1", number = "6", pages = "1704-4", }