The wave packet transform in the framework of linear canonical transform

Abstract

In this paper, we introduce the concept of linear canonical wave packet transform (LCWPT) based on the idea of linear canonical transform (LCT) and wave packet transform (WPT). Parseval’s identity and some properties of LCWPT are discussed. The inversion formula of LCWPT is formulated. Moreover, the composition of LCWPTs is defined and some properties are studied related to it. The LCWPTs of Mexican hat wavelet function are obtained.