Generalized Uncertainty Principles associated with One-Dimensional Hilbert Transform on LCT

DOI

10.2991/itoec-16.2016.7How to use a DOI?

Keywords

Uncertainty Principle; Linear Canonical Transform(LCT); Generalized Hilbert Transform (GHT); Complex Signals

Abstract

This paper discusses the Heisenberg's uncertainty principle and windowed uncertainty principle associated with 1D linear canonical transform (LCT) and the Heisenberg's uncertainty. principle associated with two types of 2D LCT for the first time. These uncertainty bounds are related with the transform parameters of LCT. Also, we show that the certainty bounds for the complex signals derived by LCT are different with that for the general complex signals in most cases. The special cases of these principles in traditional domains are provided as well. On one hand, these new uncertainty relations enrich the ensemble of uncertainty principles, and on the other hand, these derived bounds yield new understanding of complex signals via Hilbert transform.

Copyright

© 2016, 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  - Jianjun Zhou
AU  - Jie Chen
AU  - Guanlei Xu
PY  - 2016/05
DA  - 2016/05
TI  - Generalized Uncertainty Principles associated with One-Dimensional Hilbert Transform on LCT
BT  - Proceedings of the 2nd Information Technology and Mechatronics Engineering Conference (ITOEC 2016)
PB  - Atlantis Press
SP  - 28
EP  - 32
SN  - 2352-5401
UR  - https://doi.org/10.2991/itoec-16.2016.7
DO  - 10.2991/itoec-16.2016.7
ID  - Zhou2016/05
ER  -