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.
Technical Report: UTEP-CS-14-41