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Fri Apr 18 19:46:08 2008, rana, Update, ASS, check adaptive
Mon Apr 21 12:58:42 2008, rob, Update, ASS, check adaptive
Mon Apr 21 12:58:42 2008
In reply to:
Caryn Palatchi (a Caltech undergrad who just started working with us)
illustrated to me today that using even 1000 FIR taps is not very effective
for low frequency noise cancellation if you have a 2048 Hz sample rate. More
precisely, the asymptotic Wiener filter which our 'LMS' algorithm converges
to, can often
the noise at frequencies below f_sample/N_taps.
A less obvious thing that she also noticed is that there is almost no cancellation
of the 16.25 Hz bounce mode when using such a short filter. That's because that
mode is fairly high Q: the transfer function from the Z-ACC to the cavity signal
goes through the high-Q vertical suspension resonance; the FF signal we send back
goes through the low-Q horizontal pendulum response only. Therefore the filter
needs to be able to simulate ~100 cycles at 16.25 Hz in order to cancel that peak.
The message here is: we need to find a computationally efficient way to do FIR filtering
or its not going to ever be cool enough to help us find the Crab.
This is the reason for "RDNSAMP" parameter in the ASS code. The FIR filtration is applied at the downsampled rate, not the machine rate. So, if RDNSAMP=32, the effective sampling rate of the FIR filter is 64Hz, and thus noise cancellation should be good down to 64Hz/1000, or 64mHz, and the filter has an impulse response time that extends to 15 secs. I'm not convinced the filter length is what's limiting the performance at the bounce mode, but I agree that a faster FIR implementation would be good.