D. B. Percival (1991), `Characterization of Frequency Stability: Frequency Domain Estimation of Stability Measures,' Proceedings of the IEEE, 79, no. 7, pp. 961-72.
The standard characterizations of frequency stability are, in the time domain, the Allan (or two sample) variance and, in the frequency domain, the spectral density function (sdf). We describe sdf's that model sampled frequency stability data and that are related to the sdf's of the standard characterization. We review the fundamental role that sdf's play in the theory of stationary processes and processes with stationary backward differences. Based upon standard techniques in spectral analysis, we outline a systematic way of estimating sdf's typical of frequency stability data. The recommended procedure is to check for broadband bias in the periodogram using a sequence of data tapers and, if bias is in evidence, to design an autoregressive prewhitening filter to prewhiten the data. The variance of the resulting unbiased sdf estimate can be controlled either by conventional convolutional smoothers or by fitting power law models using standard regression techniques. We consider the relationship between the Allan variance and the sdf and outline two nonparametric ways of translating stability measures between the two domains - one based upon pilot analysis, and the other, upon Rutman's band-pass variance. We conclude with an example and a discussion of areas for future research.
Allan variance; Bandpass variance; Spectral estimation
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