Generate Gassian Colored Noise

2014 5 23
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更新时间：2014 5 24
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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

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Matt J
Matt J 2014-5-23
编辑：Matt J 2014-5-23

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There's MVRND, if you have the Stats Toolbox.
Otherwise, you can just do
sqrtm(R)*randn(size(R,2),1);

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S. David
S. David 2014-5-23
编辑：S. David 2014-5-23
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
Matt J 2014-5-23
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
S. David 2014-5-23
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
Matt J 2014-5-24
编辑：Matt J 2014-5-24
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
S. David 2014-5-24
编辑：S. David 2014-5-24
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?

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