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

Author

Xiang, Qiang ; Qin, Kai-Yu

Author_Institution

Coll. of Autom., Univ. of Electron., Sci. & Technol. of China, Chengdu, China

Volume

4

fYear

2011

fDate

15-17 Oct. 2011

Firstpage

2214

Lastpage

2217

Abstract

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.

Keywords

Fourier transforms; Hilbert transforms; sampling methods; Fourier transform; Hilbert transform; LCT; convolution theorem; inversion formula; linear canonical transform; linear integral transform; sampling theorem; Convolution; Educational institutions; Fourier transforms; Optical filters; Time frequency analysis; Hilbert transform; convolution theorem; linear canonical transform; sampling theorem; the Fourier transform;

fLanguage

English

Publisher

ieee

Conference_Titel

Image and Signal Processing (CISP), 2011 4th International Congress on

Conference_Location

Shanghai

Print_ISBN

978-1-4244-9304-3

Type

conf

DOI

10.1109/CISP.2011.6100605

Filename

6100605