[music-dsp] least squares harmonic model fitting

[Joshua Scholar]

Wait a second, didn't you write before that you wanted a sum of decaying
sinusoids, not pure sine waves?

----- Original Message ----- 
From: "Toth Laszlo" <tothl at inf.u-szeged.hu>
To: "music-dsp" <music-dsp at ceait.calarts.edu>
Sent: Thursday, April 07, 2005 1:41 AM
Subject: Re: [music-dsp] least squares harmonic model fitting


> On Thu, 7 Apr 2005, Joshua Scholar wrote:
>
> > Would it make sense to you to solve for LPC coefficients?
>
> Let me state the problem clearly. Let we have a signal x(t), and let we
> try to approximate it in the form
> h(t)=Sum A_i*sin(f_i*t+fi_i)
> The parameters we would like to estimate is the number of components, and
> the amplitudes, frequencies and phases of each components. We try to
> obtain these frequencies by minimizing the squared difference
> Sum_t(x(t)-h(t))^2
> In general case it is a global optimization problem. Fixing certain
> parameters however can result in much easier special cases. I'm looking
> for papers that solve EXACTLY this problem by EXACTLY this minimization in
> the general case or/and in some special cases.
>
>                Laszlo Toth
>         Hungarian Academy of Sciences         *
>   Research Group on Artificial Intelligence   *   "Failure only begins
>      e-mail: tothl at inf.u-szeged.hu            *    when you stop trying"
>      http://www.inf.u-szeged.hu/~tothl        *
>
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