Improved design of fractional order differentiator using fractional sample delay

In this paper, a digital fractional order differentiator is designed by using fractional differencing and fractional sample delay. To improve the design accuracy of the conventional fractional differencing design method at high frequency region, the integer delay is replaced by fractional sample delay. By using the well-documented FIR Lagrange and IIR allpass fractional delay filters, the proposed fractional order differentiator can be implemented easily even though the fractional sample delay is introduced. Several design examples are illustrated to demonstrate the effectiveness of the proposed method.