Uncertainty principles for hypercomplex signals in the linear canonical transform domains

Linear canonical transforms (LCTs) are a family of integral transforms with wide application in optical, acoustical, electromagnetic, and other wave propagation problems. The Fourier and fractional Fourier transforms are special cases of LCTs. In this paper, we extend the uncertainty principle for hypercomplex signals in the linear canonical transform domains, giving the tighter lower bound on the product of the effective widths of complex paravector- (multivector-)valued signals in the time and frequency domains. It is seen that this lower bound can be achieved by a Gaussian signal. An example is given to verify the result.