Synchrosqueezing-based time-frequency analysis of multivariate data

The modulated oscillation model provides physically meaningful representations of time-varying harmonic processes, and has been instrumental in the development of modern time-frequency algorithms, such as the synchrosqueezing transform. We here extend this concept to multivariate signals, in order to identify oscillations common to multiple data channels. This is achieved by introducing a multivariate extension of the synchrosqueezing transform, and using the concept of joint instantaneous frequency multivariate data. For rigor, an error bound which assesses the accuracy of the multivariate instantaneous frequency estimate is also provided. Simulations on both synthetic and real world data illustrate the advantages of the proposed algorithm.