The Ω Counter, a Frequency Counter Based on the Linear Regression
This paper introduces the Ω 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 Ω counter on rigorous mathematical basis, including the w...
| Veröffentlicht in: | IEEE transactions on ultrasonics, ferroelectrics, and frequency control. - 1986. - 63(2016), 7 vom: 26. Juli, Seite 961-9 |
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| Weitere Verfasser: | , , |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2016
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on ultrasonics, ferroelectrics, and frequency control |
| Schlagworte: | Journal Article |
| Zusammenfassung: | This paper introduces the Ω 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 Ω counter on rigorous mathematical basis, including the weighted measure and the frequency response. We describe an implementation based on a system on chip, under test in our laboratory, and we compare the Ω counter to the traditional Π and Λ counters. The LR exhibits the optimum rejection of white phase noise, superior to that of the Π and Λ 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 τ , the variance is proportional to 1/τ(2) for the Π counter, and to 1/τ(3) for both the Λ and Ω counters. However, the Ω counter has the smallest possible variance, 1.25 dB smaller than that of the Λ counter. The Ω counter finds a natural application in the measurement of the parabolic variance, described in the companion article in this Journal [vol. 63 no. 4 pp. 611-623, April 2016 (Special Issue on the 50th Anniversary of the Allan Variance), DOI 10.1109/TUFFC.2015.2499325] |
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| Beschreibung: | Date Completed 13.06.2017 Date Revised 13.06.2017 published: Print-Electronic Citation Status PubMed-not-MEDLINE |
| ISSN: | 1525-8955 |
| DOI: | 10.1109/TUFFC.2016.2570604 |