Modulated oscillations in many dimensions

Modulated oscillations are described via their timevarying amplitude and frequency. For multivariate signals, there is structure in the signal beyond this local amplitude and frequency defined for each signal component, in turn describing the commonality of the components. The multivariate structure...

Full description

Saved in:
Bibliographic Details
Published in:Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2013-02, Vol.371 (1984), p.1-21
Main Author: Olhede, S. C.
Format: Article
Language:English
Subjects:
Amplitude modulation
Dimensionality
Eigenvalues
Ellipses
Fourier transformations
Geometry
Modulated signal processing
Signal bandwidth
Time series
Trajectories
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Modulated oscillations are described via their timevarying amplitude and frequency. For multivariate signals, there is structure in the signal beyond this local amplitude and frequency defined for each signal component, in turn describing the commonality of the components. The multivariate structure encodes how the common oscillation is present in each component signal. This structure will also be evolving. I review the special case of the representation of both bivariate and trivariate oscillations. Additionally, existing results on the general multivariate oscillation are covered. I discuss the difference between a model of a multivariate oscillation compared with other common signal models of phenomena observed in several channels, and how their properties are different. I show how for the multivariate signal the global dimensionality of the signal is built up from local one-dimensional contributions, and introduce the purely unidirectional signal, to quantify how any given signal is different from the closest such signal. I illustrate the properties of the derived representation of the multivariate signal with synthetic examples, and discuss the representation of data from observations in physical oceanography.
ISSN:1364-503X