I have a device (whose behaviour I can't change) which does the following signal processing:
The incomming signal contains two frequencies $f_1$ and $f_2$. One has a huge amplitude, the other a smaller one:
$x_1 = X_{01} \cdot cos(2\pi f_1 \cdot t)$
$x_2 = X_{02} \cdot cos(2\pi f_2 \cdot t)$
with (for example):
$f_1 = 20.02e6, f_2 = 20e6, X_{01} >> X_{02}$ (Actually $f_2$ is an interfering signal).
An example for this signal (only the beating envelope is visible) is depicted below.
At first, phase durations are calculated by "measuring" the duration between two zero crossings. Then the phase duration of $f_1$ is subtracted - so if $f_2$ wouldn't be there, the phase duration signal would always be zero.
But since there is $f_2$ also, the phase duration signal contains a new periodic signal, beeing periodic with $f = f_1-f_2 = 20kHz$. I get the following signal:
With zoom
My problem is: This signal is not a pure sine wave but it contains some additional frequencies - as already visible in the zoomed phase signal. The DFT shows the containing frequencies (which are harmonics). They are depicted below.
Does anyone know an equation for the amplitudes of those frequencies as a function of the amplitude and frequency of $X_{01}$ and $X_{02}$?
To make it more complex, I unfortunaly have a second interfering signal at $f_3=19.08e6$. Is there an equation for this case, too?
