How to create Gauss noise within the interval

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

Answer 1

[Image Analyst]

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

Answer 2

[Daniel Shub]

What you are looking for is typically called a Truncated Gaussian. There is a highly rated FEX:submission

Answer 3

[Laurent]

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.