A correspondence between zeros of time-frequency transforms and Gaussian analytic functions

Rémi Bardenet (1, 2) , Pierre Chainais (1, 3) , Julien Flamant (4) , Adrien Hardy (5, 6)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
2 CNRS - Centre National de la Recherche Scientifique
3 Centrale Lille
4 CRAN - Centre de Recherche en Automatique de Nancy
5 LPP - Laboratoire Paul Painlevé - UMR 8524
6 MEPHYSTO-POST - Méthodes quantitatives pour les modèles aléatoires de la physique

In this paper, we survey our joint work on the point processes formed by the zeros of time-frequency transforms of Gaussian white noises [1], [2]. Unlike both references, we present the work from the bottom up, stating results in the order they came to us and commenting what we were trying to achieve. The route to our more general results in [2] was a sort of ping pong game between signal processing, harmonic analysis, and probability. We hope that narrating this game gives additional insight into the more technical aspects of the two references. We conclude with a number of open problems that we believe are relevant to the SampTA community.

Mots clés: time-frequency/time-scale analysis; spectrogram zeros; point process; white noise

Domaines: Traitement du signal et de l'image [eess.SP]; Probabilités [math.PR]; Statistiques [math.ST]

Rémi Bardenet, Pierre Chainais, Julien Flamant, Adrien Hardy. A correspondence between zeros of time-frequency transforms and Gaussian analytic functions. 13th International Conference on Sampling Theory and Applications, SampTA 2019, Aug 2019, Bordeaux, France. ⟨hal-02091672⟩