Monte Carlo experiment to determine the statistical uncertainty for the average 24-hour wave derived from filtered and unfiltered data

Abstract

To test whether the diurnal variation is more reliably determined from filtered data, a daily harmonic analysis is made before and after filtering an adequate sequence of synthetic bihourly values containing only random noise and a 24-hour wave of constant phase and amplitude. For each of three filters it is shown, empirically, that the statistical uncertainty of the 24-hour wave from N days of such filtered data does not differ significantly from that from N days of unfiltered data. The filters were of different bandwidths and each was designed to pass the 24-hour wave.