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To perform carrier recovery for FSK, if the data is random and can assumed to be equiprobable, then you can take the mean of the derivative of the phase versus time to determine the carrier offset.
Optionally the phase change from one sample to the next can be estimated using using a complex conjugate product of successive samples (for small angles, the ...
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I would have the easiest time explaining these briefly with the aid of an eye diagram as depicted in the graphic below.
In this example we see the constellation pattern of a raised cosine QPSK waveform on the complex plane on the left with I as the real axis and Q as the imaginary axis, and the resulting eye diagram pattern of the resulting real (I) and ...
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This is the common case for receiving spread spectrum signals since we do not know carrier frequency and phase offset but can determine that from the complex output of our correlators.
Each correlator (Early, Prompt and Late) would be complex; the complex Prompt correlator output is used for Carrier Recovery (measure rate of rotation or change in phase from ...
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You effectively want a interpolated waveform that is interpolated by 200,000 such that for each new sample with the 5 ppm offset you can select one additional offset to induce that time offset, for example
x[1], x[200,002], x[400,003], x[600,004]....
(Or equally one less if your sampling clock increased in frequency 5ppm).
One very simple approach to do ...
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The $x$-axis in the diagrams is normalized frequency (normalized by the data rate). Note that they define $S$, which is the maximum baud rate, and $S_{ave}$, which is the average baud rate. You get the maximum baud rate if your data is such that your signal is changing at a maximum rate. For NRZ-L or Manchester that would be a sequence of alternating $0$s ...
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