I would like to create complex normal Gaussian noise with dimensions $(M,N)$. The noise should be zero mean and the variance should be equal to one.
How can I do so?
$\begingroup$
$\endgroup$
$\begingroup$
$\endgroup$
You should use the the standard formula:
s = randn(m, n) + 1i*randn(m, n);
And as pointed out by MBaz, the output should be scaled accordingly by $\frac{1}{\sqrt{2}}$
s = s/sqrt(2);
More on that topic you can find for example in a book Digital Media Processing by Hazarathaiah Malepati:
It should generate exactly what you want.
-
$\begingroup$ You'll have to scale by $\frac{1}{\sqrt2}$ to get unit variance in the complex case. $\endgroup$ – David Jul 23 '15 at 11:45
-
$\begingroup$ @David can you please explain why that is?? $\endgroup$ – Wanderer Jul 23 '15 at 12:46
-
1$\begingroup$ @DimitriC The variance of a complex RV is equal to the variance of its real part plus the variance of its imaginary part. $\endgroup$ – MBaz Jul 23 '15 at 13:36
