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Instantaneous frequency and amplitude of orthocomplex modulated signals based on quaternion Fourier transform

Le Bihan, N and Sangwine, SJ and Ell, TA (2014) 'Instantaneous frequency and amplitude of orthocomplex modulated signals based on quaternion Fourier transform.' Signal Processing, 94 (1). 308 - 318. ISSN 0165-1684

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Abstract

The ideas of instantaneous amplitude and phase are well understood for signals with real-valued samples, based on the analytic signal which is a complex signal with one-sided Fourier transform. We explore the extension of these ideas to signals with complex-valued samples, using a quaternion-valued equivalent of the analytic signal obtained from a one-sided quaternion Fourier transform which we refer to as the hypercomplex representation of the complex signal. We discuss its derivation and properties and show how to obtain a complex envelope and a real phase from it. A classical result in the case of real signals is that an amplitude modulated signal may be decomposed into its envelope and carrier using the analytic signal provided that the modulating signal has frequency content not overlapping with that of the carrier. We show that this idea extends to the complex case, provided that the complex signal modulates an orthonormal complex exponential. Examples are presented to demonstrate these concepts. © 2013 Elsevier B.V.

Item Type: Article
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Faculty of Science and Health > Computer Science and Electronic Engineering, School of
Depositing User: Jim Jamieson
Date Deposited: 19 Nov 2013 16:11
Last Modified: 30 Jan 2019 16:18
URI: http://repository.essex.ac.uk/id/eprint/8527

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