Dependency of Fractional Fourier Span on Amplitude and Phase function of a Signal

-Fractional Fourier Transform is a generalization of the classical Fourier Transform, which has found its most useful applications for the transient analysis of the signals. This paper studies the span of the Fractional Fourier Transform in relation with the amplitude and phase functions of the signal and provides a mathematical derivation for the generalized case. The derived expression is shown to be useful for calculating the optimal transform order to achieve minimal possible span for various signals. Based on the derived expression, we further establish the fact that the Fractional Fourier Transform (other than the transform order of 2 π ) is most effective for the analysis of chirp signals. We provide a comparison of our method for finding optimal transform order with previously given methods and show that it provides better results. Index Terms --Fractional Fourier Transform, Generalized Bandwidth Concept, Phase and Amplitude Function, Optimal Transform Order.