Generalized Uncertainty Principles associated with One-Dimensional Hilbert Transform on LCT

摘要

This paper discusses the Heisenberg's uncertainty principle and windowed uncertainty principle associated with 1D linear canonical transform (LCT) and the Heisenberg's uncertainty principle associated with two types of 2D LCT for the first time.These uncertainty bounds are related with the transform parameters of LCT.Also,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.On one hand,these new uncertainty relations enrich the ensemble of uncertainty principles,and on the other hand,these derived bounds yield new understanding of complex signals via Hilbert transform.