  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.
