Generate Gassian Colored Noise

Hello all,

Is there any built-in function in MATLAB to generate a Gaussian noise with a specific covariance matrix R (colored noise), not necessarily the identity matrix (white noise)?

Thanks

Answer 1

[Matt J]

There's MVRND, if you have the Stats Toolbox.

Otherwise, you can just do

sqrtm(R)*randn(size(R,2),1);

[S. David]

Both are equivalent right? Because using the first method I have an error saying R must be symmetric semi-positive. It seems to be symmetric but I am not sure about semi-positive.

What is the difference between sqrt® and sqrtm®? Don't they both give the same results?

[Matt J]

It seems to be symmetric but I am not sure about semi-positive.

All covariance matrices are positive semi-definite. R therefore has to be psd in order to be a legitimate candidate.

What is the difference between sqrt® and sqrtm®?

sqrt is the elementwise square root and sqrtm is the matrix square root.

[S. David]

I am computing R numerically. May be there is some precision errors to be perfectly symmetric.

Anyway, I am using the second method.

Thanks for your answer.

[Matt J]

If R is close to singular, it can be mis-perceived as having some negative eigenvalues (and hence as not being psd) due to numerical imprecision.

However, if your R is close to singular, it really means you're taking the covariance of have some redundant variables - some of them are approximately linear combinations of the others - and should get rid of them.

[S. David]

I have two matrices, and I found the eigenvalue of both of them: one of them has all positive eigenvalues, but the other has some negative eigenvalues. I guess the second one is close to singular as you said. But even when I try the first one in mvrand(Mu,Sigma), I still get the same error.

For the matrix with negative eigenvalues, how to eliminate the redundant variables?