Simplified computation of useful functions in linear canonical transform

Bahri, Mawardi

Hilbert Journal of Mathematical Analysis
Vol. 3 No. 2 (2025): Hilbert J. Math. Anal.

The linear canonical transform is an extension of the usual Fourier transform because the Fourier transform is a special form of the linear canonical transform. It also is a valuable tool in signal analysis. Many essential properties of the Fourier transform can be transferred in the linear canonical Fourier domain with some changes. In this research paper, we first introduce the interesting connection between the linear canonical transform and Fourier transform. It is shown that the relation can be developed to efficiently evaluate Gaussian function in the linear canonical transform domain. Some examples of the Gaussian function in the linear canonical domain are also presented to illustrate the result.