Convolution, correlation and spectrum of functions associated with linear canonical transform

Abstract

The linear canonical transform (LCT), a generalization of the Fourier transform (FT), has a wide range of application domains including signal processing and optics. In this article, LCT based new convolution and correlation theorems are derived. Also discussed the real Paley–Wiener and Boas theorems, which give a characterization of two classes of functions in terms of the behaviour of their linear canonical transforms.