Re: Greg Berchin's filter design method

On Wed, 26 Apr 2006 21:21:49 +0000 (UTC), Martin Eisenberg
<martin.eisenberg@xxxxxxx> wrote:

That's a pity. Would you be comfortable with sending me a draft?

No, but in the next few days I'll try to put together some Matlab code
that implements the algorithm. Then perhaps I can make it available to
interested parties on a "not for commercial use" basis.

Otherwise, do you have any quick hints on using what you wrote back
then?

Yes; two of them.

1. Artificially adding a few samples of delay to the input data almost
always improves the least-squares fit, especially at high frequencies.
(If you use a pure cosine input and your frequency response tends toward
an odd multiple of 90° as you approach half the sampling frequency, the
output samples occur near the zero crossings and you have an
observability problem -- a "finite-input-zero-output" situation. Delay
minimizes the problem.)

2. Modifying the algorithm to perform a "weighted least squares" fit is
trivially easy. I have found that the fit can often be improved by
weighting the data by "1/magnitude" (lower magnitude => higher
weighting). Furthermore, for input data that are linearly spaced in
frequency, weighting low frequency data higher than high frequency data
is often beneficial.

Greg Berchin
.

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