A New Analytical Design Approach of Fractional Phase Advance Operator

Fractional forward filters modeling non-integer advances are digital filters, which ideally have flat group delays. This paper proposes a new, simple and efficient FIR filter design method to approximate the fractional phase advance operator z(nu). The design technique is based on the MacLaurin series expansion formula, which is applied to a discrete fractional system to obtain a closed form FIR digital filter approximation the digital ideal fractional phase advance operator z(nu) (v is an element of R+)n. Some numerical examples have been presented to illustrate the performance and the effectiveness of this new design method and its use in performing a low order digital differentiator. Some comparisons results show that the proposed design yields better performances compared to the existing techniques.