Bi-dimensional Generalized Uncertainty Relations Associated with Hilbert Transform in LCT Domain

Abstract

This paper discusses the Heisenberg’s uncertainty relations associated with two types of 2D LCT (linear canonical transform). These uncertainty bounds are related with the transform parameters of LCT. In addition, we show that the certainty bounds for the complex signals derived by LCT are different with that for the general complex signals in most cases. The special cases of these principles in traditional domains are provided as well. First, these new uncertainty relations enrich the ensemble of uncertainty principles. Second, these derived bounds yield new viewpoint of complex signals via 2D Hilbert transform.