[Numpy-discussion] def of var of complex
Robert Kern
robert.kern@gmail....
Tue Jan 8 20:56:10 CST 2008
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
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