Mathematics for Signal Processing: new results and open challenges

Antonio Cicone

Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila

Monday 10th October 2022

14:00:00

Aula Saleri - Dipartimento di Matematica

In many applied fields of research, like Geophysics, Medicine, Engineering, Economy, and Finance, to mention a few, classical challenging problems are the identification of hidden information and features contained in a given signal, like quasi-periodicities and frequency patterns, as well as the extraction of all the different components contained in it. Standard methods based on Fourier and Wavelet Transform, historically used in Signal Processing, proved to be limited in the presence of nonlinear and non-stationary phenomena. 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 several applied fields of research. In this talk, we will briefly review the pioneering technique Hilbert-Huang Transform (a.k.a. Empirical Mode Decomposition method) and discuss its known limitations. Then, we will introduce the Iterative Filtering technique and its generalizations to handle multidimensional, multivariate, or highly non-stationary signals, as well as the newly developed time-frequency representation called IMFogram. We will discuss these methods theoretical and numerical properties and show their applications to real-life data. We will conclude the talk by reviewing the main limitations of these techniques and open challenges in this research field. Contatto: roberto.piersanti@polimi.it