On the relationship between the linear canonical transform and the Fourier transform

Linear canonical transform (LCT) is a four-parameter (a,b,c,d) class of linear integral transform. It has been the focus of many research papers. In this paper, we show that the linear canonical transform is nothing more than a variation of the standard Fourier transform and, as such, many of its properties, such as its inversion formula, sampling theorems, convolution theorems and Hilbert transform can be deduced from those of the Fourier transform by a simple change of variable. Finally, An example of the application of the LCT is also given.