Linear Canonical Transform Approach to the Characteristic Function of Real Random Variables

The present research demonstrates the utility of the linear canonical transform (LCT) in constructing the characteristic function of real random variables. We refer to this construction as the linear canonical characteristic function (LCCF). The proposed LCCF aims to address the limitations of the classical characteristic function in both theoretical and applied aspects. Using this approach, we investigate its properties, such as Hermitian symmetry, continuity, convolution, and derivatives, which are generalized forms of the classical characteristic function in the literature. Finally, we implement the obtained results by calculating several probability density functions in the LCCF domains.