The whittaker-vondrak method of data smoothing as a numerical filter

We investigate the properties of the Whittaker-Vondrak method of data smoothing as a numerical filter. We obtain the theoreticlal expression relating the mixing parameter , the period P and the frequency response A, thus verifying an empirical result found by Vondrak, and generalize the expression to other definitions of “smoothness”. Using the noise spectra before and after the filter, we give the formulae for estimating the mean error per unit weight, the mean error of a filtered value, and the autocorrelation in the filtered series.