Fast ThêoBR: a method for long data set stability analysis.

ThêoBR is a high-confidence statistic that evaluates frequency stability at long τ values. However, for real-world data sets that contain thousands of points or more, the calculation of ThêoBR can take hours, days, or even weeks on a typical PC. To make the calculation of ThêoBR faster for these data sets, a method of averaging points together within the data set is developed. The error introduced by this technique is analyzed and compared with the exact value, and a correction formula is developed to minimize this error for FM noise types. Finally, the technique is applied to real data sets and determines stability at the longest τ values in seconds as opposed to weeks.