Nanohertz Frequency Determination for the Gravity Probe B HF SQUID Signal

TL;DR

This paper introduces a high-resolution frequency measurement method applied to the Gravity Probe B mission's SQUID signals, achieving nanohertz precision in frequency and decay rate determination.

Contribution

The authors developed a novel three-algorithm approach for precise frequency and decay rate measurement of sampled signals, tailored for physical phenomena modeling.

Findings

Achieved 30 nHz frequency resolution.

Attained 0.1 pHz/sec decay rate resolution.

Successfully applied to GP-B's HF SQUID signal.

Abstract

In this paper, we present a method to measure the frequency and the frequency change rate of a digital signal. This method consists of three consecutive algorithms: frequency interpolation, phase differencing, and a third algorithm specifically designed and tested by the authors. The succession of these three algorithms allowed a 5 parts in 10^10 resolution in frequency determination. The algorithm developed by the authors can be applied to a sampled scalar signal such that a model linking the harmonics of its main frequency to the underlying physical phenomenon is available. This method was developed in the framework of the Gravity Probe B (GP-B) mission. It was applied to the High Frequency (HF) component of GP-B's Superconducting QUantum Interference Device (SQUID) signal, whose main frequency fz is close to the spin frequency of the gyroscopes used in the experiment. A 30 nHz resolution in signal frequency and a 0.1 pHz/sec resolution in its decay rate were achieved out of a succession of 1.86 second-long stretches of signal sampled at 2200 Hz. This paper describes the underlying theory of the frequency measurement method as well as its application to GP-B's HF science signal.