Uncertainty principles for linear canonical transform

Authors:
Juan Zhao;Ran Tao;Yan-Lei Li;Yue Wang
Affiliations:
Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China;Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China;Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China;Department of Electronic Engineering, Beijing Institute of Technology, Beijing, China
Venue:
IEEE Transactions on Signal Processing
Year:
2009

Citing 4
Cited 9

Fractional Fourier domains

Signal Processing
Eigenfunctions of linear canonical transform

IEEE Transactions on Signal Processing
Uncertainty Principle for Real Signals in the Linear Canonical Transform Domains

IEEE Transactions on Signal Processing - Part I
An uncertainty principle for real signals in the fractional Fouriertransform domain

IEEE Transactions on Signal Processing

New inequalities for signal spreads in linear canonical transform domains

Signal Processing
On signal moments and uncertainty relations associated with linear canonical transform

Signal Processing
Generalized prolate spheroidal wave functions associated with linear canonical transform

IEEE Transactions on Signal Processing
On uncertainty principle for the linear canonical transform of complex signals

IEEE Transactions on Signal Processing
On uncertainty principle for signal concentrations with fractional Fourier transform

Signal Processing
Speech recovery based on the linear canonical transform

Speech Communication
Multi-channel filter banks associated with linear canonical transform

Signal Processing
Heisenberg's uncertainty principles for the 2-D nonseparable linear canonical transforms

Signal Processing
Sampling theorems in function spaces for frames associated with linear canonical transform

Signal Processing

Quantified Score

Hi-index	35.69

Visualization

Abstract

This correspondence investigates the uncertainty principles under the linear canonical transform (LCT). First, a lower bound on the uncertainty product of signal representations in two LCT domains for complex signals is derived, which can be achieved by a complex chirp signal with Gaussian envelope. Then, the tighter lower bound for real signals in two LCT domains proposed by Sharma and Joshi is also proven to hold for arbitrary LCT parameters based on the properties of moments for the LCT. The uncertainty principle for the fractional Fourier transform is a special case of the achieved results.