Lilly, JM and 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 |
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