Smoothing and differentiation of noisy signals are common problems whenever it is difficult or impossible to obtain derivatives by direct measurement. In biomechanics body displacements are frequently assessed and these measurements are affected by noise. To avoid high-frequency noise magnification, data filtering before differentiation is needed. In the approach reported here an autoregressive model is fitted to the signal. This allows the evaluation of the filter bandwidth and the extrapolation of the data. The extrapolation also reduces edge effects. Low-pass filtering is performed in the frequency domain by a linear phase FIR filter and differentiation is performed in the frequency domain. The reported results illustrate the accuracy of the algorithm and its speed (mainly due to the use of the FFT algorithm). Automatic bandwidth selection also guarantees the homogeneity of the results.