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

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.