Salomon M, Conklin J W, Kozaczuk J, Berberian J E, Keiser G M, Silbergleit A S, Worden P, Santiago D I
Department of Aeronautics Astronautics, Stanford University, Durand Building, 496 Lomita Mall, Stanford, California 94305-4035, USA.
Rev Sci Instrum. 2011 Dec;82(12):125110. doi: 10.1063/1.3669531.
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 signal, whose main frequency f(z) 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/s resolution in its decay rate were achieved out of a succession of 1.86 s-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.
在本文中，我们提出了一种测量数字信号频率及其频率变化率的方法。该方法由三个连续的算法组成：频率插值、相位差分，以及作者专门设计和测试的第三个算法。这三个算法的相继使用使得频率测定的分辨率达到了10的10次方分之5。作者开发的算法可应用于采样标量信号，从而能够建立一个将其主频率的谐波与潜在物理现象联系起来的模型。该方法是在引力探测器B（GP - B）任务的框架内开发的。它被应用于GP - B的超导量子干涉装置信号的高频（HF）分量，其主频率f(z)接近实验中使用的陀螺仪的自旋频率。在以2200 Hz采样的一系列时长为1.86 s的信号段中，实现了信号频率30 nHz的分辨率及其衰减率0.1 pHz/s的分辨率。本文描述了频率测量方法的基础理论及其在GP - B的HF科学信号中的应用。
