Local Fractional Z-Transforms with Applications to Signals on Cantor Sets

Abstract

The $Z$-transform has played an important role in signal processing. In this paper the $Z$-transform has been generalized by the coupling of both the $Z$-transform and the local fractional complex calculus. In the literature the local fractional $Z$-transform is applied to analyze signals, in the following it will be used to analyze signals on Cantor sets. Some examples are also given to show the efficiency and accuracy for handling the signals on Cantor sets.