On the Measurement of Frequency and of Its Sample Variance With High-Resolution Counters

Enrico Rubiola, François Vernotte, Vincent Giordano

Abstract:	A frequency counter measures the input frequency ? averaged over a suitable time t , versus the reference clock. Beside clock interpolation, modern counters improve the resolution by averaging multiple measurements highly overlapped. In the presence of white noise, the overlapping technique improves the square uncertainty from s2 ? ? 1/t 2 to s2 ? ? 1/t 3. This is important because the input trigger integrates white noise over the full instrument bandwidth, which is usually of at least 100 MHz. Due to insufficient technical information, the general user is inclined to make the implicit assumption that the counter takes the bare mean. After explaining the overlapped-average mechanism, we prove that feeding a file of contiguous data into the formula of the two-sample (Allan) variance s2 y(t ) = E{ 1 2 (yk+1 - yk)2} gives the modified Allan variance mod s2 y (t ). This conclusion is based on the mathematical reverse-engineering of the formulae found in technical specifications. More details are available on the web site arxiv.org, document arXiv:physics/0411227 [1]. Our purpose is to warn the experimentalists against possible mistakes, and to encourage the manufacturers to explain what the instruments really do.
Published in:	Proceedings of the 37th Annual Precise Time and Time Interval Systems and Applications Meeting August 29 - 31, 2005 Vancouver, Canada
Pages:	46 - 49
Cite this article:	Rubiola, Enrico, Vernotte, François, Giordano, Vincent, "On the Measurement of Frequency and of Its Sample Variance With High-Resolution Counters," Proceedings of the 37th Annual Precise Time and Time Interval Systems and Applications Meeting, Vancouver, Canada, August 2005, pp. 46-49.
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