Sviluppo e analisi di tecniche innovative per lo studio di segnali non stazionari.

Many real-life signals present time-varying features like frequency, amplitude and oscillatory patterns, and can be contaminated by random patterns like noise and artifact. These are called non-stationary signals and many algorithms exist to study and decompose them, one being Fast Iterative Filtering (FIF). In this work we first present an in depth description of FIF in Chapter 2, with an application of one of its extensions in Chapter 3. After that, we will tackle the problem of extending FIF to spherical domains, Chapter 4. In particular, by leveraging the Generalized Locally Toeplitz sequence theory in Chapter 5, we are able to characterize spectrally the operators associated with the spherical extension of Iterative Filtering, Chapter 6. Finally, we propose a convergent extension of Iterative Filtering, called Spherical Iterative Filtering, and present numerical results of its application to spherical data in Chapter 7.