Uncertainty principles for the two‐sided offset quaternion linear canonical transform

Abstract

The offset quaternion linear canonical transform (OQLCT) provides a more general framework for a number of linear integral transforms in signal processing and optics, such as quaternion Fourier transform (QFT), fractional quaternion Fourier transform (FrQFT), and linear canonical transform (QLCT). We devote this paper to various different of uncertainty principles (UPs) for the two‐sided OQLCT, which including logarithmic UP, Heisenberg‐type UP, Hardy's UP, Beurling's UP, Entropic UP, Donoho‐Stark's UP, and Local UP. Moreover, we also prove Lieb's UP for the two‐sided short‐time offset quaternion linear canonical transform (SOQLCT).