I have the following problem:(adsbygoogle = window.adsbygoogle || []).push({});

I measure a sinusoidally varying signal at a number of phase points. I then fit a sine curve to the data points using least squares. The fitting function looks like:

f = a1 + a2 cos(phi) + a3 sin(phi)

I want to evaluate the modulation depth from the measurements given by

m = sqrt(a2*a2 + a3*a3)/a1

Now the problem is that mean(m) is a biased estimator of m, and this becomes very significant when the signal-to-noise ratio is low. This would seem like a pretty common type of problem but I'm not a stat guy. Can someone please point me in the right direction, literature, web site, anything that could help me out here?

Johannes

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# Unbiased estimator of modulation depth?

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