F-Transform Enhancement of the Sampling Theorem and Reconstruction of Noisy Signals

Authors

Michal Holčapek, University of OstravaFollow
Irina Perfilieva, University of OstravaFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

5-2014

Comments

Technical Report: UTEP-CS-14-41

Abstract

According to a sampling theorem, any band-limited and continuous signal can be uniquely reconstructed from certain of its values. We show that a reconstruction can be obtained from the set of F-transform components and moreover, the sampling theorem follows as a particular case. A special attention is paid to the case where sample values of a signal come with noise. We show that in the presence of noise, a more accurate reconstruction than that based on the sampling theorem can be obtained, if instead of noised sample values the F- transform components of the signal with respect to a generalized fuzzy partition are used.