caa a22 4500 605496420 CHVBK 20210128100536.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10231-014-0406-6 doi (NATIONALLICENCE)springer-10.1007/s10231-014-0406-6 Space-frequency analysis in higher dimensions and applications [Elektronische Daten] [Yan Yang, Pei Dang, Tao Qian] In the Clifford algebra setting of Euclidean spaces, monogenic signals are naturally defined as the boundary limit functions of the associated monogenic functions in the related domain. In an earlier paper, we defined a scalar-valued phase derivative as a candidate of instantaneous frequency of a multivariate signal. In this paper, we obtain fundamental relations between such defined phase derivative and the Fourier frequency. The results generalize the latest results of quadrature phase derivative in one-dimensional to multi-dimensional cases in the Clifford algebra setting. We also prove two uncertainty principles in higher dimensions of which one is for scalar-valued signals and the other is for vector-valued signals with the axial form. Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 Monogenic signals nationallicence Frequency nationallicence Hilbert transform nationallicence Poisson kernel nationallicence Gauss Kernel nationallicence Uncertainty principle in higher dimensions nationallicence Yang Yan School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, China aut Dang Pei Department of General Education, Macau University of Science and Technology, Macao, Taipa, China aut Qian Tao Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao, Taipa, China aut Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/4(2015-08-01), 953-968 0373-3114 194:4<953 2015 194 10231 https://doi.org/10.1007/s10231-014-0406-6 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-014-0406-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Yang Yan School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, China aut NATIONALLICENCE 700 1- Dang Pei Department of General Education, Macau University of Science and Technology, Macao, Taipa, China aut NATIONALLICENCE 700 1- Qian Tao Department of Mathematics, Faculty of Science and Technology, University of Macau, Macao, Taipa, China aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/4(2015-08-01), 953-968 0373-3114 194:4<953 2015 194 10231