The novel Clifford-valued quadratic-phase wave packet transform and its applications

In order to represent the Clifford valued signals more efficiently in the time-frequency plane, we propose a novel integral transform known as Clifford quadratic-phase wave packet transform based on the convolution operator associated with the Clifford quadratic-phase Fourier transform. The article begins by deriving the fundamental properties of the proposed transform such as linearity, parity, dilation, and orthogonality relation. Furthermore, some vital results of harmonic analysis have been established like energy conservation, inversion formula, and characterization of range. Then we proceed by obtaining the uncertainty principles for the transform including Heisenberg’s and logarithmic uncertainty principles. The essential part of the paper deals with the discussion of an illustrative example and several potential applications.