%0 Journal Article
%T Bivariate Instantaneous Frequency and Bandwidth
%A Jonathan M. Lilly
%A Sofia C. Olhede
%J Physics
%D 2009
%I arXiv
%R 10.1109/TSP.2009.2031729
%X 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.
%U http://arxiv.org/abs/0902.4111v2