# How to create Gauss noise within the interval

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David Kusnirak on 17 Sep 2013
I have an interval with lower boundary at a = -0.005 and upper boundary b = 0.005. I need to create the Gauss white noise within this interval. For uniformly distributed pseudorandom numbers (generated by rand) it is clear e.g.:
r = a + (b-a).*rand(100,1);
however it does not work for randn function.I need some way how to produce the Gaussian noise in given interval. Is there any way how to do it?
thanks
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### Accepted Answer

Image Analyst on 17 Sep 2013
One (inefficient) way is to just create more than you need and throw away any outside the range. Of course this might make it not purely Gaussian anymore
% Generate the numbers.
mu=2;
sigma = 4;
r = mu + sigma .* randn(1000,1);
% Define range we want
a = -7;
b = 9;
badNumbers = r < a | r > b;
r(badNumbers) = [];
numberOfElementsNow = numel(r)
% Define how many you need
numElementsNeeded = 400;
% Get them
if numElementsNeeded < numberOfElementsNow
r = r(1:numElementsNeeded);
numberOfElementsNow = numel(r)
else
% Tack some more on and try again.
end
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### More Answers (2)

Daniel Shub on 17 Sep 2013
What you are looking for is typically called a Truncated Gaussian. There is a highly rated FEX:submission
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Laurent on 17 Sep 2013
This is not possible, since the output of randn can be in principle any value between -Inf and +Inf.
Depending on what you want you could set the width of the gaussian to a reasonable value (for example sigma=0.005) and then later clip values outside of your interval to the border values.
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