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The Allan variance has historically been estimated using heterodyne measurement systems, which have low noise and preserve the carrier phase information needed for long-term stability. The single-sideband phase noise has traditionally been estimated using phase detectors that suppress the carrier to achieve even lower noise. The recent development of the direct-digital phase noise measurement technique makes it possible to estimate both statistics accurately and simultaneously from the same time series of the phase. Our comparison of the 3 techniques has revealed several challenges to the accurate estimation of the Allan variance including undesired aliasing, biased estimators, and spurious signal generation. Investigation of these difficulties has led to several opportunities to improve Allan variance estimation, including the ability to estimate the instrumentation noise floor during a measurement and the existence of an optimum measurement bandwidth. In the end, this has led to faster, easier, more reliable, and more accurate measurement methods.

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