The Linear Canonical Transform and Time-Frequency Representations

DOI

10.2991/emim-15.2015.144How to use a DOI?

Keywords

Linear canonical transform; Wigner distribution; Time-frequency representation; Short-time Fourier transform

Abstract

The linear canonical transform(LCT), which is a generalization of the classical Fourier transform and fractional Fourier transform(FRFT), was introduced a number of years ago in the mathematics literature but appears to have remained largely unknown to the signal processing community, to which it may, however, be potentially useful. In this paper, we briefly introduce the LCT and a number of its properties and then discuss the LCT’s relationships with time-frequency representations such as the Wigner distribution and the short-time Fourier transform. These relationships have a very simple and natural form and show that the LCT performs a homogeneous linear mapping in the time-frequency plane. Finally, an example of the application of the LCT is given.

Copyright

© 2015, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Qiang Xiang
PY  - 2015/04
DA  - 2015/04
TI  - The Linear Canonical Transform and Time-Frequency Representations
BT  - Proceedings of the 2015 International Conference on Education, Management, Information and Medicine
PB  - Atlantis Press
SP  - 728
EP  - 733
SN  - 2352-5428
UR  - https://doi.org/10.2991/emim-15.2015.144
DO  - 10.2991/emim-15.2015.144
ID  - Xiang2015/04
ER  -