The Omega Counter, a Frequency Counter Based on the Linear Regression
Abstract
This article introduces the {\Omega} counter, a frequency counter -- or a frequency-to-digital converter, in a different jargon -- based on the Linear Regression (LR) algorithm on time stamps. We discuss the noise of the electronics. We derive the statistical properties of the {\Omega} counter on rigorous mathematical basis, including the weighted measure and the frequency response. We describe an implementation based on a SoC, under test in our laboratory, and we compare the {\Omega} counter to the traditional {\Pi} and {\Lambda} counters. The LR exhibits optimum rejection of white phase noise, superior to that of the {\Pi} and {\Lambda} counters. White noise is the major practical problem of wideband digital electronics, both in the instrument internal circuits and in the fast processes which we may want to measure. The {\Omega} counter finds a natural application in the measurement of the Parabolic Variance, described in the companion article arXiv:1506.00687 [physics.data-an].
Cite
@article{arxiv.1506.05009,
title = {The Omega Counter, a Frequency Counter Based on the Linear Regression},
author = {E. Rubiola and M. Lenczner and P. -Y. Bourgeois and F. Vernotte},
journal= {arXiv preprint arXiv:1506.05009},
year = {2015}
}
Comments
8 pages, 6 figure, 2 tables