System control and identification often require the accurate estimation of velocity and acceleration with areduced group delay and lowpass property to attenuate high-frequency noise. This paper proposes a novel FIRfilter for velocity and acceleration estimation, where the filter coefficients are derived by piecewise Radial Basis Function Network (RBFN). The proposed FIR filter achieves the prescribed lowpass property, and the specified group delay in passband. It is shown that the frequency response of the FIR filter converges to the ideal frequency response which is derived by the theoretical analysis of periodic RBFN in the frequency domain. Finally, the procedures for designing the filter are summarized with a design example.
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