When processing measurement data, it is usually assumed that some amount of normally distributed measurement noise is present. In some situations, outliers are present in the measurements and consequently the noise is far from normally distributed. In this case classical least-squares procedures for estimating Fourier spectra (or derived quantities like the frequency response function) can give results which are inaccurate or even useless. In this paper, a novel technique for the on-line processing of measurement outliers will be proposed. Both the computation speed and the accuracy of the technique presented will be compared with different classical approaches for handling outliers in measurement data (i.e. filtering techniques, outlier rejection techniques and robust regression techniques). In particular, all processing techniques will be validated by applying them to the problem of speckle drop-out in optical vibration measurements (performed with a laser Doppler vibrometer), which typically causes outliers in the measurements.