ABSTRACT
We analyze the Allan variance estimator as the combination of discrete-time linear filters. We apply this analysis to the different variants of the Allan variance: the overlapping Allan variance, the modified Allan variance, the Hadamard variance and the overlapping Hadamard variance. Based upon this analysis, we present a new method to compute a new estimator of the Allan variance and its variants in the frequency domain. We show that the proposed frequency domain equations are equivalent to extending the data by periodization in the time domain. Like the total variance, which is based on extending the data manually in the time domain, our frequency domain variance estimators have better statistics than the estimators of the classical variances in the time domain. We demonstrate that the previous well-know equation that relates the Allan variance to the power spectrum density (PSD) of continuous-time signals is not valid for real world discrete-time measurements and we propose a new equation that relates the Allan variance to the PSD of the discrete-time signals and allows computation of the Allan variance and its different variants in the frequency domain.
ABSTRACT
This paper is devoted to the study of the symmetry of the Rabi pedestal of the clock transition in an optically pumped Cs beam frequency standard. The frequency of the microwave oscillator is locked on the center of the Rabi pedestal using a square wave frequency modulation. We observe a modulation of the center frequency as a function of the modulation depth. Experimental investigations on this unexpected effect are reported.
