[music-dsp] least squares harmonic model fitting

robert bristow-johnson rbj at audioimagination.com
Fri Apr 8 10:57:40 EDT 2005

on 04/08/2005 03:48, Toth Laszlo at tothl at inf.u-szeged.hu wrote:

> On Thu, 7 Apr 2005, robert bristow-johnson wrote:
>> well, you *could* try googling these words: sinusoidal modeling least
>> squares (without quotes).  you'll get lots of hits.
> Of course I did, but couldn't exactly get what I was looking for.

some of those hits looked interesting to me.  se la vie.
>> when the frequencies are known, this is a straight forward problem
>> (especially for least squares),
> I would need a reference on this. This is what my colleagues did, and I'm
> also sure that it is known, but I can't find a reference on.

well, i dunno a reference other than a textbook one on least squares or
Fourier Series.  i'll look at the old George-Smith paper and see if they put
one in.

Joshua seemed to have the gist of it.  effectively, you fit the windowed
sines and cosines of the know frequencies to your windowed input signal,
square and add up your windowed difference, take partial derivatives w.r.t.
your sin/cos coefficients and set them to zero (for minimization), and you
will get a set of linear equations that you have to solve (say, with
Gaussian elimination).


r b-j                  rbj at audioimagination.com

"Imagination is more important than knowledge."

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