On the Study of Interference and their Localization in the Time-Frequency Plane

Sylvain Meignen (1) , Thomas Oberlin (2)

1 DAO - Données, Apprentissage et Optimisation
2 ISAE-SUPAERO - Institut Supérieur de l'Aéronautique et de l'Espace

In this paper, our goal is first to investigate the conditions for the separation of the modes making up multicomponent signals based on the analysis of the short-time Fourier transform. More precisely, we put forward necessary and sufficient conditions for the existence of ridges associated with the modes in the time-frequency plane. The focus is put on signals either made of purely harmonic modes or parallel linear chirps, for which we show that when the modes are strongly interfering in the time-frequency plane, the ridges no longer exist and are replaced by some structures called time-frequency bubbles. Based on a careful study of interference patterns, we show that the zeros of the spectrogram involved in these share very specific features, on which we found a new algorithm to determine interference locations based on the Delaunay triangulation of spectrogram zeros.

Mots clés: Time-frequency analysis; short-time Fourier transform; spectrogram zeros; Delaunay triangulation

Domaines: Recherche d'information [cs.IR]; Analyse fonctionnelle [math.FA]

Sylvain Meignen, Thomas Oberlin. On the Study of Interference and their Localization in the Time-Frequency Plane. 2021. ⟨hal-03327526⟩