### New advances on the decomposition and analysis of nonstationary signals: a Mathematical perspective on Signal Processing.

- Series
- Applied and Computational Mathematics Seminar
- Time
- Monday, December 5, 2022 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Antonio Cicone – University of L'Aquila

In many applied fields of research, like Geophysics, Medicine, Engineering, Economy, and Finance, to name a few, classical problems are the extraction of hidden information and features, like quasi-periodicities and frequency patterns, as well as the separation of different components contained in a given signal, like, for instance, its trend.

Standard methods based on Fourier and Wavelet Transform, historically used in Signal Processing, proved to be limited when nonlinear and non-stationary phenomena are present. For this reason in the last two decades, several new nonlinear methods have been developed by many research groups around the world, and they have been used extensively in many applied fields of research.

In this talk, we will briefly review the Hilbert-Huang Transform (a.k.a. Empirical Mode Decomposition method) and discuss its known limitations. Then, we will review the Iterative Filtering technique and we will introduce newly developed generalizations to handle multidimensional, multivariate, or highly non-stationary signals, as well as their time-frequency representation, via the so-called IMFogram. We will discuss the theoretical and numerical properties of these methods and show their applications to real-life data.

We will conclude the talk by reviewing the main problems which are still open in this research field.