Offset Linear Canonical Wavelet Transforms

Abstract

This study extends the one-dimensional offset linear canonical transform (OLCT) to n-dimensionalOLCT and establishes a significant connection between the traditional Fourier transform and the OLCT.We present the Parseval identity for the OLCT in n-dimensions. Furthermore, the offset linear canonicalwavelet (OLCW) with special rotation and the offset linear canonical wavelet transform (OLCWT) withspecial rotation are introduced. The OLCT of the OLCW is computed and, using it, the inner-product relation of the OLCWT and the corresponding reconstruction formula are obtained. A relationship between theOLCT of a function and OLCT of its derivative is derived, which is then applied to differential equationsand an inequality of the uncertainty principle type.