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Back in the days when whatever digital filter you had for processing
of exploration seismic data made a difference in whether you got a
job or not, we were in the heat of it. My guys found the research
report listed below and we implemented the Martin-Graham concept
of digital filters.
Auburn Research Foundation
Auburn, AL
Contract NA8-5164 for George C. Marshall Space Flight Center
The report: "Digital Filters" by Edward B. Anders, et.al. concluded
that the Martin-Graham filter design was the OPTIMUM design to
minimize Gibbs effect as a function of roll-off rate and length of
operator.
Sorry I cannot find the report but I'll assure you that these filters
are the optimum for the parameters defined.
Maybe someone has access to these solutions and can provide
the math/code needed.
Clyde
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Clyde Lee Chairman/CEO (Home of SwingMachine)
SYTECH Corporation email: clydelee@xxxxxxxxxxxx
7910 Westglen, Suite 105 Office: (713) 783-9540
Houston, TX 77063 Fax: (713) 783-1092
Details at: www.theswingmachine.com
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----- Original Message -----
From: "Alex Matulich" <alex@xxxxxxxxxxxxxx>
To: <omega-list@xxxxxxxxxx>
Sent: Tuesday, July 06, 2004 12:18 AM
Subject: More Fun With Filters
This message regards the code I posted earlier, that will output either a
normal 2nd-order Butterworth lowpass filter or a critically-damped lowpass
filter, and optionally cascade them for you.
I figured out that combining the two types of filters results in an
improvement over both. Here's what you need:
* A 2-pass critical damping filter of a given length L
* A 1-pass normal Butterworth of length L*2/3
(both of which are available from the code I posted).
If you plot these, you'll see that the overshoot of the Butterworth can be
balanced by the lag of the critically-damped filter. Averaging the two
together, you get a filter that:
* has negligible overshoot (it has a little but it can be tuned out; the
2/3 length multiplier was derived by eyeballing the chart)
* preserves the same fall-off in the frequency spectrum as a length-L
Butterworth
* has a sharper roll-off than either the Butterworth or critically-damped
filter.
The only problem that remains is the fact that the critically damped
filter blows up below a certain value of L. For the 2-pass critical
damping filter, it blows up when L<=4.6, and starts ringing around L=9.2,
so you wouldn't want the length to be less than 9.2. There's some
adjustment that needs to be put in the formula somewhere but I haven't
figured out what it is.
The first picture attached shows the 2-pass critical damping filter of
length 40, and a 1-pass 2nd-order Butterworth of length 40*2/3, showing
how the lag of one balances the overshoot of the other.
The second picture shows the frequency spectrum of the filters.
Those of you who get the digest with no attachments should be able to see
them in the purebytes.com archives.
THIS is why I don't make money trading! I keep getting distracted by
these experiments.
-Alex
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