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Message ID: 394
Entry time: Sat Mar 22 22:39:02 2008

Author: 
mevans 
Type: 
Summary 
Category: 
CDS 
Subject: 
Direct Form 2 filters are bad 


Here I show a comparison between the filter algorithm currently used in LIGO (Direct Form II), and an alternative algorithm designed to reduce numerical noise. The input signal is
x = sin(2 * pi * t) + 1e9 * sin(2 * pi * (fs / 4) * t);
where fs = 16384 is the sample rate. The filter is a 4th order notch at 1Hz (f_poles = f_zeros = 1Hz, Q_poles = 1, Q_zeros = 1e6). It is clear that the DF2 algorithm produces a noise floor that is, for this simple filter, 1e11 / rtHz smaller than the input drive amplitude (see plots). That should probably be scary given how many secondordersections we run our signals through. The lownoise form does a somewhat better job. The lownoise algorithm has the same memory and computational requirements as DF2, and our CDS guys have the code in hand. I suggest we start testing soon.
(The code is included below. You will need my Matlab library to run the top level test script.) 



Attachment 3: 
FiltRT.zip
1 kB
Uploaded Mon Mar 24 14:07:26 2008
 