|Abstract: ||Recent advances in time-frequency theory have led to the development of high resolution time-frequency algorithms, such as the empirical mode decomposition (EMD) and
the synchrosqueezing transform (SST). These algorithms provide enhanced localization in representing time varying oscillatory components over conventional linear and quadratic time-frequency algorithms. However, with the emergence of low cost multichannel sensor technology, multivariate extensions of time-frequency algorithms are needed in order to
exploit the inter-channel dependencies that may arise for multivariate data. Applications
of this framework range from filtering to the analysis of oscillatory components.
To this end, this thesis first seeks to introduce a multivariate extension of the synchrosqueezing transform, so as to identify a set of oscillations common to the multivariate
data. Furthermore, a new framework for multivariate time-frequency representations is developed using the proposed multivariate extension of the SST. The performance of the proposed algorithms are demonstrated on a wide variety of both simulated and real world
data sets, such as in phase synchrony spectrograms and multivariate signal denoising.
Finally, multivariate extensions of the EMD have been developed that capture the
inter-channel dependencies in multivariate data. This is achieved by processing such data directly in higher dimensional spaces where they reside, and by accounting for the power
imbalance across multivariate data channels that are recorded from real world sensors, thereby preserving the multivariate structure of the data. These optimized performance
of such data driven algorithms when processing multivariate data with power imbalances and inter-channel correlations, and is demonstrated on the real world examples of Doppler radar processing.|