Nanohertz Frequency Determination for the Gravity Probe B HF SQUID Signal

摘要

In this paper, we present a method to measure the frequency and the frequencychange rate of a digital signal. This method consists of three consecutivealgorithms: frequency interpolation, phase differencing, and a third algorithmspecifically designed and tested by the authors. The succession of these threealgorithms allowed a 5 parts in 10^10 resolution in frequency determination.The algorithm developed by the authors can be applied to a sampled scalarsignal such that a model linking the harmonics of its main frequency to theunderlying physical phenomenon is available. This method was developed in theframework of the Gravity Probe B (GP-B) mission. It was applied to the HighFrequency (HF) component of GP-B's Superconducting QUantum Interference Device(SQUID) signal, whose main frequency fz is close to the spin frequency of thegyroscopes used in the experiment. A 30 nHz resolution in signal frequency anda 0.1 pHz/sec resolution in its decay rate were achieved out of a succession of1.86 second-long stretches of signal sampled at 2200 Hz. This paper describesthe underlying theory of the frequency measurement method as well as itsapplication to GP-B's HF science signal.