Neal Becker wrote: > 2 is what I expected. Suppose I have a complex signal x, with additive > Gaussian noise (i.i.d, real and imag are independent). > y = x + n
Not only do the real and imag marginal distributions have to be independent, but also of the same scale, i.e. Re(n) ~ Gaussian(0, sigma) and Im(n) ~ Gaussian(0, sigma) for the same sigma. > Consider an estimate \hat{x} = y. > > What is the mean-squared-error E[(y - x)^2] ? > > Definition 2 is consistent with that, and gets my vote. Ah, you have to be careful. What you wrote is what is implemented. Definition 2 is consistent with this, instead: E[|y - x|^2] But like I said, I see no particular reason to favor circular Gaussians over the general form for the implementation of numpy.var(). -- Robert Kern "I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth." -- Umberto Eco _______________________________________________ Numpy-discussion mailing list Numpy-discussion@scipy.org http://projects.scipy.org/mailman/listinfo/numpy-discussion