Planar sampling sets for the short-time Fourier transform

Philippe Jaming (1) , Michael Speckbacher

1 IMB - Institut de Mathématiques de Bordeaux

This paper considers the problem of restricting the short-time Fourier transform to domains of nonzero measure in the plane and studies sampling bounds of such systems. In particular, we give a quantitative estimate for the lower sampling bound in the case of Hermite windows and derive a sufficient condition for a large class of windows in terms of a certain planar density. On the way, we prove a Remez-type inequality for polyanalytic functions. MSC2010: 42C40, 46E15, 46E20, 42C15 Revised according to referee's recomandation

Mots clés: short-time Fourier transform; concentration estimates; planar sets of sampling; polyanalytic Bargmann-Fock spaces; irregular Gabor frames; Remez-type inequalities; sampling sets; poly- analytic Bargmann-Fock spaces

Domaines: Analyse classique [math.CA]; Analyse fonctionnelle [math.FA]; Variables complexes [math.CV]

Philippe Jaming, Michael Speckbacher. Planar sampling sets for the short-time Fourier transform. Constructive Approximation, 2021, 53, pp.479-502. ⟨10.1007/s00365-020-09503-4⟩. ⟨hal-02147705v2⟩