New Uncertainty Principles in the Linear Canonical Transform Domains Based on Hypercomplex Functions

In this paper, we obtain uncertainty principles associated with the linear canonical transform (LCT) of hypercomplex functions. First, we derive the uncertainty principle for hypercomplex functions in the time and LCT domains. Moreover, we exploit the uncertainty principle in two LCT domains. The lower bounds are related to the LCT parameters and the covariance, and the uncertainty principle presented herein is sharper than what has been presented in the existing literature.These tighter bounds can be obtained using hypercomplex chirp functions for a Gaussian envelope. Finally, we verify the validity of the uncertainty principles through some examples and discuss several potential applications of the new results in signal processing.