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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) + 1e-9 * 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, 1e-11 / rtHz smaller than the input drive amplitude (see plots). That should probably be scary given how many second-order-sections we run our signals through. The low-noise form does a somewhat better job. The low-noise 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 1: low-noise_filtering.png  26 kB  | Hide | Hide all
low-noise_filtering.png
Attachment 2: low-noise_zoom.png  19 kB  | Hide | Hide all
low-noise_zoom.png
Attachment 3: FiltRT.zip  1 kB  Uploaded Mon Mar 24 14:07:26 2008
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