Linear canonical wavelet transform and linear canonical wave packet transform on the Schwartz type spaces

In this paper, we enlarge the domain of the linear canonical wavelet transform and linear canonical wave packet transform to generalized functions. We construct suitable Schwartz type spaces and these transforms are then proved to be homeomorphisms from the Schwartz space onto their corresponding Schwartz type spaces. Using the bi-continuity, these transforms are extended to tempered distribution space by adjoint method. As an application to signal processing, we then compute the linear canonical wave packet transform of a signal distribution. An example of the linear canonical wave packet transform of a Dirac delta function is specified.