2004/11/30 by Enrico Rubiola · 2 citations
Physics and Astronomy · #physics.ins-det
paper · pdf · doi:10.1063/1.1898203
published as Review of Scientific Instruments vol. 76 no. 5 art. no. 054703, may 2005 · 14 pages, 5 figures, 1 table, 18 references
arxiv created 2004/12/31 · arxiv updated 2009/12/01
A frequency counter measures the input frequency ν averaged over a suitable time τ, versus the reference clock. High resolution is achieved by interpolating the clock signal. Further increased resolution is obtained by averaging multiple frequency measurements highly overlapped. In the presence of additive white noise or white phase noise, the square uncertainty improves from \smashσ2ν∝1/τ2 to \smashσ2ν∝1/τ3. Surprisingly, when a file of contiguous data is fed into the formula of the two-sample (Allan) variance \smashσ2y(τ)=𝔼\\frac12(yk+1-yk) 2\ of the fractional frequency fluctuation y, the result is the modified Allan variance mod σ2y(τ). But if a sufficient number of contiguous measures are averaged in order to get a longer τ and the data are fed into the same formula, the results is the (non-modified) Allan variance. Of course interpretation mistakes are around the corner if the counter internal process is not well understood.