Generalized wave packet transform based on convolution operator in the quaternion quadratic-phase Fourier domain

The classical quaternion quadratic-phase Fourier transform fails in locating the quaternion quadratic-phase domain frequency contents that is required in numerous applications. In order to address this drawback, we in this paper proposed a novel transform coined as quaternion quadratic-phase wave packet transform (Q-QPWPT). The preliminary findings are the derivation of fundamental properties like linearity, parity, scaling, dilation and orthogonality relation. Moreover, some key harmonic analysis results like energy conservation, inversion formula and characterization of range are obtained. Besides, we also derived the Heisenberg’s and logarithmic uncertainty principles. The crux of the paper lies in presenting an illustrative example and some potential applications.