  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 on 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 \cite{totvar}, which is based on extending
the data manually in the time domain, our frequency domain variances 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 that allows to compute the Allan variance and its different
variants in the frequency domain .
