Uncertainty Principles for Linear Canonical Transform

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.