  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.
