Octonion short‐time linear canonical transform

Abstract

We investigate the octonion short-time linear canonical transform (OCSTLCT) in this paper. First, we propose the new definition of the OCSTLCT, and then several important properties of newly defined OCSTLCT, such as bounded, shift, modulation, time-frequency shift, inversion formula, and orthogonality relation, are derived based on the spectral representation of the octonion linear canonical transform (OCLCT). Second, by the Heisenberg uncertainty principle for the OCLCT and the orthogonality relation property for the OCSTLCT, the Heisenberg uncertainty principle for the OCSTLCT is established. Finally, we give an example of the OCSTLCT.

Discrete Octonion Linear Canonical Transform: Definition and Properties

“…We [32] substituted the octonion Fourier kernel function with the octonion linear canonical kernel function and obtained the octonion linear canonical transform (OCLCT). Next, some papers [32,33] discussed many properties and uncertainty principles associated with the OCLCT. Moreover, many scholars [34,35] proposed different transform forms of the OCLCT.…”