NDLI: A revisit of the unique polar representation of the Vector-valued Hyperanalytic Signal

Content Provider	IEEE Xplore Digital Library
Author	Boqiang Huang
Copyright Year	2015
Description	Author affiliation: Inst. fur Math., Univ. Paderborn, Paderborn, Germany (Boqiang Huang)
Abstract	In this paper, we extend the classic analytic signal to the Vector-valued Hyperanalytic Signal (VHaS) that is denoted to distinguish from the multivariate hypercomplex data. The 2d-Dimensional (2d-D) VHaS, S(t) : [0,1] → $C_{2d},$ is defined by a complexification of two d-D Vector-valued Hypercomplex Signals (VHcS), S(t) := $G(t)e_{0}$ + $H^{C2d}_{ed}[G](t)$ $e_{d},$ where $H^{C2d}_{ed}$ and $e_{i}$ represent the Hilbert transform and the $i_{th}$ unit axis, and G(t) ϵ $C_{d},$ $e_{i}$ G $C_{2d}.$ Inspired by the unique polar form of a classic analytic signal and the one of a 4-D VHaS proposed in the work of Huang and Kunoth (2014), we provide a theoretical explanation of the unique polar representation of a 6-D or 8-D VHaS by replacing the quaternion with octonion, which further implies the possible extension for d-D VHaS with d> 8. Moreover, the derived continuous VHcS envelope and phase from the polar form lead to a unified definition of the time-frequency-amplitude spectrum of the given VHcS G(t).
Starting Page	1172
Ending Page	1176
File Size	287537
Page Count	5
File Format	PDF
ISBN	9780992862633
ISSN	20761465
DOI	10.1109/EUSIPCO.2015.7362568
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-08-31
Publisher Place	France
Access Restriction	Subscribed
Rights Holder	EURASIP
Subject Keyword	Vector-valued hypercomplex signal Quaternions Quaternionic signal Oc-tonionic signal Europe Time-frequency-amplitude spectrum Vector-valued hyperanalytic signal Transforms Signal processing Brain modeling Arrays Unique polar representation
Content Type	Text
Resource Type	Article

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