On Uncertainty Principle for Quaternionic Linear Canonical Transform

Abstract EN

We generalize the linear canonical transform (LCT) to quaternion-valued signals, known as the quaternionic linear canonical transform (QLCT).

Using the properties of the LCT we establish an uncertainty principle for the QLCT.

This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains.

It is shown that only a 2D Gaussian signal minimizes the uncertainty.