Fractional fourier transform of generalized functions

Abstract

In recent years the fractional Fourier transform (FRFT), which is a generalization of the Fourier transform, has been the focus of many research papers because of its application in several areas, including signal processing and optics. In this paper, we extend the fractional Fourier transform to different spaces of generalized functions using two different techniques, one analytic and the other algebraic. The algebraic approach requires the introduction of a new convolution operation for the fractional Fourier transform that makes the transform of a convolution of two functions almost equal to the product of their transform.