Adaptive Multiscale Time-Frequency Analysis

Abstract

Time-frequency analysis techniques are now adopted as standard in many applied fields, such as bio-informatics and bioengineering, to reveal frequency-specific and time-locked event-related information of input data. Most standard time-frequency techniques, however, adopt fixed basis functions to represent the input data and are thus suboptimal. To this cause, an empirical mode decomposition (EMD) algorithm has shown considerable prowess in the analysis of nonstationary data as it offers a fully data-driven approach to signal processing. Recent multivariate extensions of the EMD algorithm, aimed at extending the framework for signals containing multiple channels, are even more pertinent in many real world scenarios where multichannel signals are commonly obtained, e.g., electroencephalogram (EEG) recordings. In this chapter, the multivariate extensions of EMD are reviewed and it is shown how these extensions can be used to alleviate the long-standing problems associated with the standard (univariate) EMD algorithm. The ability of the multivariate extensions of EMD as a powerful real world data analysis tool is demonstrated via simulations on biomedical signals.