polarization framework for bivariate signal processing

Bivariate signals appear in a broad range of applications: polarized waveforms in seismology and optics, current velocities in oceanography, etc. Formally, bivariate signals are 2D vector time series. Existing approaches for bivariate signal processing do not provide a straightforward description of the signal in terms of its polarization properties. For this purpose we introduce a new and generic framework for processing bivariate signals. It is based on a tailored quaternion Fourier transform enabling the generalization of usual signal processing quantities such as spectral densities, analytic signals or spectrograms. This new framework re-establishes a clear interpretability in terms of polarization attributes.
In this talk, I will introduce the main features of this approach and illustrate its usefulness on synthetic and real-world data from geophysics and gravitational wave physics.