The Ω Counter, a Frequency Counter Based on the Linear Regression
Résumé
This article introduces the counter, a frequency counter - i.e., a frequency-to-digital converter - based on the Linear Regression (LR) algorithm on time stamps. We discuss the noise of the electronics. We derive the statistical properties of the 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 counter to the traditional and counters. The LR exhibits optimum rejection of white phase noise, superior to that of the and 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. With a measurement time , the variance is proportional to 1=2 for the counter, and to 1=3 for both the and counters. However, the counter has the smallest possible variance, 1.25 dB smaller than that of the counter. The counter finds a natural application in the measurement of the Parabolic Variance (PVAR), described in the companion article [1] IEEE Transact. UFFC vol. 63 no. 4 pp. 611-623, April 2016 (Special Issue on the 50th Anniversary of the Allan Variance).