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Bob:
>But you can design filters in either domain. The two domains are
>simply a different abstract representation of the same thing, just
>as are the photograph and topographic maps images of Mount Everest.
Now that I have come up with a generalized way to construct any
arbitrary 2-pole polynomial filter with no zeros[1], I have an
opportunity to design an "optimum" filter in Excel using the
builtin Solver, using both the time domain and frequency domain
characteristics. The solver can diddle with the filter coefficients
while maximizing a score of filter performance.
The only problem is coming up with meaningful performance measures,
and scoring them so that the solver can minimize it.
One performance measure might be the attenuation one octave and two
octaves from the 3dB cutoff frequency (more attenuation = higher
score). That's a frequency domain measurement.
In the time domain, one might choose to measure the amount of
overshoot on a step function (less overshoot = higher score),
combined with the speed at which the filter output intersects the
step (less time = higher score).
What performance measures would you suggest, and how do you suppose
they might be combined?
-Alex
Footnotes:
[1] I added the generalized 2-pole filter recipe to the bottom of
http://unicorn.us.com/trading/2polefilters.html
I'm also working on a generalized 4-pole polynomial filter.
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