The calculation of Grnwald-Letnikov's(G-L) weighted coefficient of first-order approximation has an accurate and fast recursive formula, while the calculation of Lubich's weighted coefficient of high-order approximation has a high complexity and a long calculation time. The approximation order of Lubich operator is proved by Fourier transform, and a class of Weighted Shifted Lubich Difference(WSLD) operators of fourth order approximation is proposed based on shifted Lubich operators. Then, the filtering characteristics of WSLD operator are analyzed from the perspective of digital signal processing, and a fractional digital Finite Impulse Response(FIR) differential filter based on WSLD operator is designed and verified by numerical simulation. Compared with Al-Alaoui and Lubich, the results show that the algorithm using WSLD operator to solve the filter coefficient of fractional digital FIR filter is simple and efficient, and can effectively reduce the influence of Gibbs effect compared with other operators.