Tighter uncertainty principles for linear canonical transform in terms of matrix decomposition

Abstract

Uncertainty principles of the linear canonical transform (LCT) are of importance in optics and signal processing. Thanks to the positive definite property of the spread matrix for arbitrary signals, this study discusses the lower bound of uncertainty product of complex signals in two LCT domains through using this matrix's rotation orthogonal decomposition mainly. We formulate two kinds of lower bounds, which are tighter than the existing ones proposed respectively by Xu et al and Dang et al. We obtain sufficient and necessary conditions that give rise to these sharper results truly, and propose quantitative indexes to analyze the difference with the existing bounds. Then we reduce the derived uncertainty principle inequalities to the time and LCT domains and to the two fractional Fourier transform (FRFT) domains. Examples and numerical simulations are also carried out to verify the correctness of the theoretical analyses. Finally, we discuss the new proposals' application in the estimation of the effective bandwidth encountered in optical systems, time–frequency analysis, and affine modulation schemes.