According to my measurements I conclude that LSC-signal is retarded from OMC-signal with the constant retarded time of 92usec.
It means there are no timing jitter between them. Only a constant time-delay exists.
Let's begin with basics.
If you measure the same signal at OMC-side and LSC-side, they can have some time delay between them. It can be described as followers.
where tau_0 is the time delay. If the tau_0 is not constant, it causes a noise of the timing jitter.
I have injected the sine-wave with 200.03Hz into the OMC-LSC_DRIVE_EXC. Then by using get_data, I measured the signal at 'OMC-LSC_DRIVE_OUT' and 'LSC-DARM_ERR' where the exciting signal comes out.
In the ideal case the two signals are completely identical.
In order to find the delay, I calculated the difference in these signals based on the method described by Waldman. The method uses the following expression.
Here the tau_s is the artificial delay, which can be adjusted in the off line data.
By shifting tau_s we can easily find the minimal point of the RMS, and at this point we can get tau_0=tau_s.
This is the principle of the method to measure the delay. In my measurement I put T=1sec. and make the calculation every 1sec. in 1 min.
Attachment is the obtained results. The above shows the minimum RMS sampled every 1sec. and the below shows the delay in terms of number of shifts.
1 shift corresponds to Ts (=1/32kHz). All of the data are matched with 3 times shift, and all of the minimum RMS are completely zero.
Therefore I can conclude that LSC-signal is retarded from OMC-signal with constant retarded times of 3*Ts exactly, and no timing jitter has been found.