Re: estimation of autocorrelation matrix or eigenvalue spread.
- From: "Rune Allnor" <allnor@xxxxxxxxxxxx>
- Date: 11 Aug 2006 07:56:55 -0700
Andor wrote:
Rune Allnor wrote:
...
The other question was whether you can achieve the same
goals with other means than eigenvalues. You could try to
compute the AR(P) model for some fixed P and estimate
the ration between the geometric and arithmetic means
of the magnitudes of the zeros.
Interesting. Why the ratio of the geometric and arithmetic means of the
magnitudes? I would have guessed that an estimate for the eigenspread
of the signal is the square of the ratio of the max and the min of the
magnitudes of the zeros of the prediction polynomial.
First: This has nothing at all to do with the eigenvalues, at least not
in a way I am aware of. It has to do with spectrum flatness. The OP
wanted to evaluate how well the equalizer worked, this is an
alternative
approach that may or may not be a bit cheaper to compute.
If you have a flat spectrum the zeros of the AR predictor tend to
be distributed evenly around the unit circle at fairly similar
magnitudes, say, around 0.5. Both the geometric and arithmetic
means may be fairly low here.
If you have a spectrum with lots of peaks, sone zeros are close to
the unit circle in order to cancel those peaks. The ratio between
the arithmetic and geometric means is nonlinear, and capable of
picking up that difference, even if there is only one or two poles that
have moved.
Both the AIC and MDL order estimators for AR models use this
concept.
Rune
.
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