## How to create a complex normal i.i.d.?

Gn Gnk

### Gn Gnk (view profile)

님이 질문을 제출함. 27 Oct 2019
최근 활동 Gn Gnk

### Gn Gnk (view profile)

님이 댓글을 추가함. 27 Oct 2019
John D'Errico

### John D'Errico (view profile)

님이 답변을 채택함.
Hello ,
i want to create a i.i.d CN(0,σ^2)
I create the variable like that :
x=sqrt(var/2)*(randn+1i*randn);
Is this correct?

Bjorn Gustavsson

### Bjorn Gustavsson (view profile)

27 Oct 2019
Does that satisfy your definition of a complex normal distribution? Does it fit with for example the definitions here: Complex_normal_distribution?
Gn Gnk

### Gn Gnk (view profile)

27 Oct 2019
I just want to know how to convert it to matlab code and if this : x=sqrt(var/2)*(randn+1i*randn);
is correct or not.
Thank you.

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## 답변 수: 1

John D'Errico

### John D'Errico (view profile)

님의 답변 27 Oct 2019
채택된 답변

Is it correct? It is what it is. You are creating a rotationally symmetric complex random variable, where if we define the variance to be
N = 1e7;
V = 3;
X = sqrt(V/2)*(randn(N,1) + i*randn(N,1));
Does it have zero mean? That is trivial, yes. The population mean is clearly zero, and the sample mean will approach zero as N-->inf.
Xbar = mean(X)
Xbar =
0.0002026 - 0.00027059i
Vbar = (X-Xbar)'*(X - Xbar)/(N-1)
ans =
2.999
As you can see, the sample variance seems to approach 3. I could spend some time to verify the expected value of that result for the population, done in symbolic form. But I can as easily just say that is is "correct".

Gn Gnk

### Gn Gnk (view profile)

27 Oct 2019
Thank you a lot sir!

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