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I have two Gaussian noise generators, from MATLAB's randn() function:

noise1 = randn(1,100000)
noise2 = randn(1,100000)

I'm finding the points where they are equal. For this, I add 100 points in between each point:

mehvec = linspace(1,100000,100*(100000-1));
meh1 = [];
meh2 = [];
for i = 2:1:n
    meh1 = [meh1, linspace(noise1(i-1),noise1(i),100)];
    meh2 = [meh2, linspace(noise2(i-1),noise2(i),100)];
end

Now, I scan each point, to see if there's a sign change in the difference between the two noises, where the sign change occurs, and what the noise value is when they're equal:

diff = meh1 - meh2;
crossvec = [];
valuevec = [];
for i = 2:1:length(mehvec)
    if diff(i-1)>=0 && diff(i)<0 || diff(i-1)<0 && diff(i)>=0
        crossvec = [crossvec,i];
        valuevec = [valuevec,meh1(i)];
    end
end

The result is supposed to be Gaussian because, like actual thermal noise, these are supposed to be samples of Gaussian white noise. There is a problem in the Gaussianity, in the vector where the instantaneous noises are equal. Where is it coming from?

Here's the normal-probability plot of the values where they're equal. It should be a straight line (which indicates Gaussianity), but it isn't. The code used to generate it is:

figure;
set(gcf,'color','w');
normplot(meh1(crossvec));

Here's the normal-probability plot of the values where they're equal. It should be a straight line (which indicates Gaussianity), but it isn't.

Christiana S. F. Chamon
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    You need to define `n` and possibly other variables in your code so we can run it. Also, the code for the normal probability plot is missing (`normplot(valuevec)`?). Lastly, and most importantly: why do you think the result should be Gaussian? Is there some theoretical result that ensures it? – Luis Mendo Dec 23 '20 at 17:26
  • I have never heard of this property, could you include a reference for where it is proven? – Cris Luengo Dec 23 '20 at 17:49
  • I would think that extreme values are less likely than for normally distributed values, and so your result makes sense to me. – Cris Luengo Dec 23 '20 at 18:00
  • @CrisLuengo I had the same intuition, but in the shown graph extreme values are _more_ likely – Luis Mendo Dec 23 '20 at 18:22
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    @Luis: You’re right. That’s a weird effect. – Cris Luengo Dec 23 '20 at 18:40

0 Answers0