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.