Add gaussian distributed noise with mean and variance to matrix

Hello,

I've seen that to add gaussian distributed noise to a matrix A with mean 0 and var = 5, this is the code

A_wnoise = A + 5*randn(size(A))

Now, how do you add noise with mean 5 and var = 5 to the matrix A? Thanks.

Answer 1

[Image Analyst]

A_wnoise = A + 5*randn(size(A)) + 5;

[Alexander Kocian]

The accepted answer is wrong because the square root is missing.

A_wnoise = A + sqrt(variance)*randn(size(A)) + meanValue;

[Image Analyst]

You are correct. I overlooked that part when I copied his code - I just added the desired mean value to the end of it. Thanks for catching/correcting it.

[Deryk Smith]

What if your variance is supposed to be (0:0.1:10)? the code does not work then.

[Image Analyst]

Variance can't be an array. However you can put one variance into randn() and put it into a loop over all variances to get a family of arrays.

Answer 2

[Muhammad Yasir]

How can I generate a noise sequence w_t, which is i.i.d. Gaussian of mean zero with variance 2I3 (2xI3 ,where I3 is identity matrix of dimension 3x3) and the initial condition is x_init = [10 10 −10]'

[Image Analyst]

I don't know what the initial condition is. But it looks like you have 3 variances so you can get three sets of random numbers. Is this what you want?

numberOfSamples = 99000; % Whatever.
% Define initial parameters.
x_init = [10, 10, -10]'
variances = 2 * eye(3)
% Compute additional needed parameter:
stdDeviations = sqrt(variances)
% Loop, getting 3 sets of sample numbers drawn from a Normal distribution.
for row = 1 : size(variances, 2)
	w_t = x_init(row) + stdDeviations(row, row) * randn(1, numberOfSamples);
	% Double check and print out
	fprintf('For sample set #%d, mean = %f, variance = %f, and standard deviation = %f.\n',...
		row, mean(w_t), var(w_t), std(w_t));
end

[Muhammad Yasir]

Thank you for addressing my query and sharing the code.

I am actually trying to simulate algorithams given in a research paper.

Kindly look at this segment of the paper for which I need to create Gaussian noise samples. I think gaussian noise is a column vector...

[Image Analyst]

Since this is not an Answer to @monkey_matlab's original question, can you post this as a new question?

[Muhammad Yasir]

OK, I will do that...

[Image Analyst]

"OK, I will do that..." <== I just checked and it's not there yet.

[Muhammad Yasir]

Sorry, I could post it immediately. I have posted this question as per your advice. Here is the link to my Query:

https://uk.mathworks.com/matlabcentral/answers/878528-how-to-generate-iid-gaussian-noise-vector