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Spectral analysis of clock noise: a primer

The statistical characterization of clock noise is important for understanding how well a clock can perform in applications where timekeeping is important. The usual frequency domain characterization of clock noise is the power spectrum. We present a primer on how to estimate the power spectrum of clock noise given a finite sequence of measurements of time (or phase) differences between two clocks. The simplest estimator of the spectrum is the periodogram. Unfortunately this estimator is often problematic when applied to clock noise. Three estimators that overcome the deficiencies of the periodogram are the sinusoidal multitaper spectral estimator, Welch's overlapped segment averaging estimator and Burg's autoregressive estimator. We give complete details on how to calculate these three estimators. We apply them to two examples of clock noise and find that they all improve upon the periodogram and give comparable results. We also discuss some of the uses for the spectrum and its estimates in the statistical characterization of clock noise.