Clifford-valued linear canonical wave-packet transform and corresponding uncertainty principles

Abstract

In an effort to express Clifford-valued signals efficiently in time–frequency domain, we introduce the notion of the novel integral transform known as Clifford-valued linear canonical wave-packet transform (CLCWPT). In the beginning, we derived the fundamental properties of the proposed transform which include linearity, anti-linearity, scaling parity, dilation and Parseval’s formula. Moreover, some important signal analysis results have been established, viz. energy conservation, inversion formula, characterization of range and bounds of clifford valued linear canonical wave-packet transform. We culminate our manuscript by studying corresponding Heisenberg’s uncertainty principle and logarithmic uncertainty principle associated with CLCWPT.