The uncertainty associated with the weighted mean frequency of a phase-stabilized signal with white phase noise

Abstract

The weighted mean is widely used in combining data sets of experimental measurements with a weight proportional to the value of the data number divided by the sample variance in a conventional method. However, this standard procedure is not appropriate for obtaining the weighted mean frequency of a phase-stabilized signal with white phase noise, since the data are autocorrelated. The autocorrelation is obtained in the case of white phase noise and a new weighting method is proposed. Using this, the uncertainty associated with the weighted mean frequency of a phase-stabilized signal with white phase noise is given. The effect of counter dead-time is also discussed.