A New Class of Linear Canonical Wavelet Transform

Abstract

We define a new class of linear canonical wavelet transform (LCWT) and study its properties like inner product relation, reconstruction formula and also characterize its range. We obtain Donoho-Stark’s uncertainty principle for the LCWT and give a lower bound for the measure of its essential support. We also give the Shapiro’s mean dispersion theorem for the proposed LCWT.

Keywords

• linear canonical transform
• linear canonical wavelet transform
• uncertainty principle
• shapiro’s theorem