The Class of Bandlimited Functions with Unstable Reconstruction under Thresholding

Holger Boche (1) , Ullrich J. Mönich (1)

1 Heinrich-Hertz-Chair for Mobile Communications

The reconstruction of PW1-functions by sampling series is not possible in general if the samples are disturbed by the non-linear threshold operator which sets all samples whose absolute value is smaller than some threshold to zero. In this paper we characterize the set of functions for which the sampling series diverges as the threshold goes to zero and show that this set is a residual set.

Domaines: Analyse classique [math.CA]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Holger Boche, Ullrich J. Mönich. The Class of Bandlimited Functions with Unstable Reconstruction under Thresholding. SAMPTA'09, May 2009, Marseille, France. pp.General session. ⟨hal-00453084⟩