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Bivariate Instantaneous Frequency and Bandwidth

Lilly, JM; Olhede, SC; (2010) Bivariate Instantaneous Frequency and Bandwidth. IEEE T SIGNAL PROCES , 58 (2) 591 - 603. 10.1109/TSP.2009.2031729.

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Abstract

The generalizations of instantaneous frequency and instantaneous bandwidth to a bivariate signal are derived. These are uniquely defined whether the signal is represented as a pair of real-valued signals or as one analytic and one anti-analytic signal. A nonstationary but oscillatory bivariate signal has a natural representation as an ellipse whose properties evolve in time, and this representation provides a simple geometric interpretation for the bivariate instantaneous moments. The bivariate bandwidth is shown to consist of three terms measuring the degree of instability of the time-varying ellipse: amplitude modulation with fixed eccentricity, eccentricity modulation, and orientation modulation or precession. An application to the analysis of data from a free-drifting oceanographic float is presented and discussed.

Type: Article
Title: Bivariate Instantaneous Frequency and Bandwidth
DOI: 10.1109/TSP.2009.2031729
Keywords: Amplitude and frequency modulated signal, analytic signal, instantaneous bandwidth, instantaneous frequency, multivariate time series, OCEAN CURRENT SPECTRA, VALUED TIME-SERIES, ANALYTIC SIGNAL, WAVELET, POLARIZATION, KINEMATICS, AMPLITUDE, VORTICES, PHASE, EDDY
UCL classification: UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science
URI: http://discovery.ucl.ac.uk/id/eprint/168772
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