芦野 隆一

This paper deals with the linear canonical wavelet transform. It is a non-trivial generalization of the ordinary wavelet transform in the framework of the linear canonical transform. We first present a direct relationship between the linear canonical wavelet transform and ordinary wavelet transform. Based on the relation, we provide an alternative proof of the orthogonality relation for the linear canonical wavelet transform. Some of its essential properties are also studied in detail. Finally, we explicitly derive several versions of inequalities associated with the linear canonical wavelet transform.

In our previous work, we established some basic poverties of the linear canonical transform and obtained alternative form of convolution and correlation theorems. In this paper, we study essential properties of the linear canonical transform (LCT). The properties are modifications of the classical Fourier transform properties. They are very need in applying LCT in signal processing. In addition, we formulate an inequality associated with the LCT, which is different from the uncertainty principle in literature.