Fast Iterative Filtering: a new, fast and robust decomposition method for nonlinear and nonstationary processes

The analysis of nonlinear and nonstationary processes is, in general, a challenging task.
One way to tackle it is to first decompose the signal into simpler components and then analyze them separately. This is the idea behind the Empirical Mode Decomposition (EMD) method, published originally in 1998. EMD had a big impact in many filed of research as testified by the more than 15300 citations (based on Scopus). However, the mathematical properties of EMD and its generalizations, like the Ensemble EMD, are still under investigation. For this reason an alternative technique, called Iterative Filtering (IF), was proposed in 2009.

In this talk we introduce the IF method and present new insights in its mathematical properties. In particular, we show its robustness to noise, its ability to avoid mode mixing, and its speed up in what is called the Fast Iterative Filtering (FIF).
Both IF and FIF have been extened to handle multivariate and multidimensional data sets, outperforming, in terms of computational time, any alternative method proposed so far in the literature for the decomposition of nonstationary signals.

This is a joint work with H. Zhou (Georgia Tech).