Nanohertz Frequency Determination for the Gravity Probe B HF SQUID Signal

Details Nanohertz Frequency Determination for the Gravity Probe B HF SQUID Signal Nanohertz Frequency Determination for the Gravity Probe B HF SQUID Signal

2011-11-19

arxiv.org/abs/1111.4521v1

Physics

Instrumentation and Detectors

The following article has been submitted to Review of Scientific Instruments. After it is published, it will be found at (http

Scientific paper

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.

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