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Analysis of modulated multivariate oscillations

Lilly, JM; Olhede, SC; (2012) Analysis of modulated multivariate oscillations. IEEE Transactions on Signal Processing , 60 (2) pp. 600-612. 10.1109/TSP.2011.2173681.

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The concept of a common modulated oscillation spanning multiple time series is formalized, a method for the recovery of such a signal from potentially noisy observations is proposed, and the time-varying bias properties of the recovery method are derived. The method, an extension of wavelet ridge analysis to the multivariate case, identifies the common oscillation by seeking, at each point in time, a frequency for which a bandpassed version of the signal obtains a local maximum in power. The lowest-order bias is shown to involve a quantity, termed the instantaneous curvature, which measures the strength of local quadratic modulation of the signal after demodulation by the common oscillation frequency. The bias can be made to be small if the analysis filter, or wavelet, can be chosen such that the signal's instantaneous curvature changes little over the filter time scale. An application is presented to the detection of vortex motions in a set of freely drifting oceanographic instruments tracking the ocean currents. © 2011 IEEE.

Type: Article
Title: Analysis of modulated multivariate oscillations
DOI: 10.1109/TSP.2011.2173681
Keywords: Amplitude and frequency modulated signal, analytic signal, Bedrosian's theorem, complex-valued signal, complex-valued time series, multivariate signal
UCL classification: UCL > School of BEAMS > Faculty of Maths and Physical Sciences
UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science
URI: http://discovery.ucl.ac.uk/id/eprint/1304599
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