Kit Ian Kou, Jian-Yu Ou, and Joao Morais, On Uncertainty Principle for Quaternionic Linear Canonical Transform, Hindawi Publishing Corporation, Abstract and Applied Analysis, Volume 2013, Article ID 725952, 14 pages, DOI: 10.1155/2013/725952. Open Access: http://www.hindawi.com/journals/aaa/2013/725952/, Full Text PDF: http://downloads.hindawi.com/journals/aaa/2013/725952.pdf
Abstract: We generalize the linear canonical transform (LCT) to quaternion-valued signals, known as the quaternionic linear canonical transform (QLCT). Using the properties of the LCT we establish an uncertainty principle for the QLCT. This uncertainty principle prescribes a lower bound on the product of the effective widths of quaternion-valued signals in the spatial and frequency domains. It is shown that only a 2D Gaussian signal minimizes the uncertainty.
Source: Email by Kit Ian Kou, kikou_AT_umac.mo 30 Oct. 2013, http://www.hindawi.com/journals/aaa/2013/725952/