- #1
f91jsw
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I have the following problem:
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
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