Analytic signal in many dimensions - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2018

Analytic signal in many dimensions


In this paper we extend analytic signal to the multidimensional case. First it is shown how to obtain separate phase-shifted components and how to combine them into instantaneous amplitude and phase. Secondly we define the proper hypercomplex analytic signal as a holo-morphic hypercomplex function on the boundary of polydisk in the hypercomplex space. Next it is shown that the correct phase-shifted components can be obtained by positive frequency restriction of the Scheffers-Fourier transform based on the commutative and associative algebra generated by the set of elliptic hypercomplex numbers. Moreover we demonstrate that for d > 2 there is no corresponding Clifford-Fourier transform that allows to recover phase-shifted components correctly. Finally the euclidean-domain construction of instantaneous amplitude is extended to manifold and manifold-like graphs and point clouds.
Fichier principal
Vignette du fichier
Tsistvero.ACHA.2018.pdf (5.1 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-01877403 , version 1 (19-09-2018)



Mikhail Tsitsvero, Pierre Borgnat, Paulo Gonçalves. Analytic signal in many dimensions. 2018. ⟨hal-01877403⟩
104 View
208 Download



Gmail Mastodon Facebook X LinkedIn More