Design of a fractional zero-phase filter based on liouville-weyl integral

In viewpoint of noncausal and non-integeral dimensional signal processing, a novel and computationally efficient, fractional zero-phase FIR filter is proposed by a definition of Liouville-Weyl fractional integrator. Based on two commonly used Liouville and Weyl fractional integral definitions, we present Liouville fractional linear phase delay filter and Weyl fractional linear phase lead filter. Thanks to the reverse phase characteristics of Weyl fractional filter, an overall zero-phase effect can be achieved by paralleling a Liouville fractional filter with a Weyl fractional filter. Due to the inherent characteristics of fractional integrals, the designed filter is good at removing additive noise as well as preserving signal detail information. Numerical examples are demonstrated to illustrate the performance of the proposed design method and show that our method has larger design flexibility than the conventional integer integral-based methods.