Ricerc@Sapienza

I segnali modulati in frequenza appaiono in molte discipline applicate, tra cui la geologia, la comunicazione, la biologia e l'acustica. Questi sono multicomponenti, cioè consistono in forme d'onda multiple, con frequenza specifica dipendente dal tempo (frequenza istantanea). Nella maggior parte delle applicazioni pratiche, il numero di modalità - che è sconosciuto - è necessario per analizzare correttamente un segnale; per esempio per separare ogni singolo componente e per stimare la sua frequenza istantanea.

Instantaneous frequency (IF) is a fundamental feature in multicomponent signals analysis and its estimation is required in many practical applications. This goal can be successfully reached for well separated components, while it still is an open problem in case of interfering modes. Most of the methods addressing this issue are parametric, that is, they apply to a specific IF class. Alternative approaches consist of non-parametric time filtering-based procedures, which do not show robustness to destructive interference---the most critical scenario in crossing modes.

The paper presents a first attempt to correct the time-frequency reassignment of a multicomponent signal having non separable individual components. In particular, the case of a 2-components signal has been investigated in depth. It has been proved that the integral (along frequencies) of the spectrogram is still a multicomponent signal with specific instantaneous frequencies. As a result, the spectrogram of this signal allows us to disentangle the frequencies and recover the missing information in the non separability region.