System control and identification often require accurate estimations of velocity and acceleration with a reduced group delay and low-pass property to attenuate high frequency noise. This paper proposes a novel design method of FIR filter for estimating velocity and acceleration from sampled displacement data, where the filter coefficients are derived by piecewise Radial Basis Function Network (RBFN). The proposed FIR filter not only provides more accurate estimates when compared to the conventional method, but also achieves the prescribed low-pass property and specified group delay in the pass band. The theoretical analysis of RBFN in the frequency domain reveals the relationship between the frequency response of the FIR filter and width/regularization parameters in the RBFN. Finally, the procedures for designing the filter are summarized with design examples.