Fractional 90° phase‐shift filtering based on the double‐sided Grünwald–Letnikov differintegrator
Jianhong Wang, Yongqiang Ye, Xudong Gao · IET Signal Processing · 2015
A fractional 90° phase‐shift filtering technique is investigated based on the double‐sided Grünwald–Letnikov differintegrator. Thanks to the Grünwald–Letnikov definition of fractional calculus, first the left and the right‐sided Grünwald–Letnikov differintegrators are presented, which are generalised magnitude‐and‐phase modulations. Then, parallel a left‐sided Grünwald–Letnikov differintegrator with a right‐sided Grünwald–Letnikov differintegrator to obtain a double‐sided Grünwald–Letnikov differintegrator, which is essentially a fractional 90° phase‐shift filter with the capability of noise immunity. A double‐sided symmetrical convolution mask is constructed to implement the proposed fractional 90° phase shifter. Finally, a singularity detection example is illustrated to demonstrate that the proposed double‐sided Grünwald–Letnikov differintegrator is forward 90°, which is the same as the conventional first‐order differential, and possesses good noise immunity that can be tuned by adjusting the differintegral order.