In this work we show that powers of two multiples of the sampling period are the optimal set of averaging period Allan variance (AVAR) calculations for determining power law noise types present in recorded data. The primary merit of AVAR is that it indicates the slopes associated with each of the power law noise types as well as the level of each type included, even for a mixture of noise types. We show that unlike other arbitrary series, the powers-of- two values are spectrally the closest-to-independent set of AVAR values possible, and thus optimally decompose frequencies in such a way as to have the least uncertainty in estimating slopes. We further demonstrate the unique property of this choice of averaging period series by proving the equivalence between the sums of the powers-of-two values of the non-overlapping Allan variance and twice the value of the standard variance.
April 14-18, 0019
2019 IEEE International Frequency Control Symposium IFCS-EFTF
Allan Variance, Power Law Noise Determination, Stability Characterization, Standard Variance, Statistical Theory