Bivariate Instantaneous Frequency and Bandwidth

Details Bivariate Instantaneous Frequency and Bandwidth Bivariate Instantaneous Frequency and Bandwidth

2009-02-24

arxiv.org/abs/0902.4111v2

Lilly, J. M., and S. C. Olhede (2010). Bivariate instantaneous frequency and bandwidth. IEEE Transactions on Signal Processing

Statistics

Methodology

Scientific paper

10.1109/TSP.2009.2031729

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.

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