Using Koji's mathematica notebook, and Nic's python work, I set out to run a time domain simulation of the error signal, with band-limited white noise added in.
Basically, I sweep the displacement of the cavity (with no noise), and pass it to the analytical formulae with the coefficients Koji used, with some noise added in. I also included some 1/0 protection for the linearized PDH signal. I ran a sweep, and then compared it to an ALS sweep that Jenne ran on Monday; reconstructing what the CESAR signal would have looked like in the sweep.
The noise amounts were totally made up.
They matched up very well, qualitatively! [Since the real sweep was done by a (relatively) noisy ALS, the lower noise of the real pdh signal was obscured.]
Given this good match, we were motivated to start trying to implement it on Monday.
At this point, since we've gotten it working on the actual IFO, I don't plan on doing much more with this simulation right now, but it may come in handy in the future...