Re: Spectrum analysis question

On Sun, 28 Sep 2008 22:49:29 -0500, "emre" <eguven@xxxxxxxxxxx> wrote:

James,

The right answer to your question depends on the distribution of the
noise, and exactly what you want to do.

If you are assuming i.i.d. complex (circular) Gaussian noise, than its
amplitude has Rayleigh distribution. Given multiple observations, all the
information is summarized in the "sufficient statistic", which is the sum
of squared magnitudes.

This is why you would like to average the squared magnitudes: It gives
you the Maximum Likelihood Estimator (MLE) for the power spectral density
of complex Gaussian noise. MLE is invariant under transformations, that
means, the MLE of the magnitude is the square root of the sum of squared
magnitudes. The MLE is asymptotically unbiased and efficient. As the
sample size goes to infinity, MLE achieves the minimum mean squared error
among all possible estimators.

If you are concerned with estimating the power spectral density in the
above case, the MLE (averaging sum of squared magnitudes) is better because
it gives you the uniformly minimum variance unbiased estimator. Squaring
the sum of magnitudes gives you an inadmissible estimator.

Hope this helps.

Emre

Hello,
Thank you Emre.

JDH

.

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