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The Ω Counter, a Frequency Counter Based on the Linear Regression.

Enrico Rubiola, Michel Lenczner, Pierre-Yves Bourgeois

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    Summary

    The new Ω counter, a frequency counter using linear regression (LR), offers superior white phase noise rejection compared to traditional counters. It achieves the smallest variance, making it ideal for precise frequency measurements.

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    Area of Science:

    • Electrical Engineering
    • Signal Processing
    • Metrology

    Background:

    • White phase noise is a significant challenge in wideband digital electronics.
    • Existing frequency counters (Π and Λ) have limitations in noise rejection and variance.

    Purpose of the Study:

    • Introduce the Ω counter, a novel frequency counter based on the linear regression (LR) algorithm.
    • Analyze the statistical properties and performance of the Ω counter.
    • Compare the Ω counter's performance against traditional Π and Λ counters.

    Main Methods:

    • Developed a frequency counter utilizing the linear regression (LR) algorithm on time stamps.
    • Derived rigorous mathematical properties, including weighted measure and frequency response.
    • Implemented the Ω counter on a system on chip for laboratory testing.

    Main Results:

    • The LR algorithm in the Ω counter demonstrates optimal rejection of white phase noise.
    • The Ω counter exhibits a variance proportional to 1/τ(3), outperforming the Π counter (1/τ(2)).
    • The Ω counter achieves the smallest variance, 1.25 dB lower than the Λ counter.

    Conclusions:

    • The Ω counter provides superior performance in rejecting white phase noise, a critical issue in digital electronics.
    • Its mathematical rigor and implementation show a significant advancement over existing frequency counters.
    • The Ω counter is well-suited for applications like parabolic variance measurement.