Data driven sampling of oscillating signals

Brigitte Bidégaray-Fesquet (1) , Marianne Clausel (2)

1 EDP - Equations aux Dérivées Partielles
2 SAM - Statistique Apprentissage Machine

The reduction of the number of samples is a key issue in signal processing for mobile applications. We investigate the link between the smoothness properties of a signal and the number of samples that can be obtained through a level crossing sampling procedure. The algorithm is analyzed and an upper bound of the number of samples is obtained in the worst case. The theoretical results are illustrated with applications to fractional Brownian motions and the Weierstrass function.

Mots clés: monoHölderian functions; Level crossing sampling; oscillations

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Analyse fonctionnelle [math.FA]; Statistiques [math.ST]; Théorie [stat.TH]; Analyse numérique [math.NA]

Brigitte Bidégaray-Fesquet, Marianne Clausel. Data driven sampling of oscillating signals. Sampling Theory in Signal and Image Processing, 2014, 13 (2), pp.175-187. ⟨10.1007/BF03549578⟩. ⟨hal-00905184v2⟩