According to Z-transform representations of discrete B-Spline functions

the fitting and decomposing of the signal in B-Spline space can be implemented by FIR filters and IIR filters. Based on that and variational calculus

the B-Spline filter constructed to determine the mean line in surface roughness measurement comes into being. The difference equations for B-Spline filter is deduced by the technique of zero phase shift filtering. The experiment in the surface profile of a workpiece validate this method. The B-Spline filter also bears the characteristic of zero phase shift and has more computing efficiency than other methods.