White Noises Generation in Matlab

Hi, I'm writing a function for the simulation of a multi-correlated random process with autoregressive filters' method. So I need to generate M white noises, being M the process dimension. I've tried using both "randn" and "mvnrnd", but the white noises seems to be not perfectly unrelated. In fact both the coherence functions and the cross-spectrums are not zero. This affects the simulated process' quality, which is more correlated than I expect. So, is there a better way to generate an M dimensional process of unrelated white noises?

Answer 1

[Daniel Shub]

This isn't really a MATLAB question, I think your understanding of random processes is a little off. If you generate finite length random samples from two uncorrelated random processes you will find that the correlation is not exactly zero. As the length of the sample increases the correlation will decrease.

[Lapo]

Hi Daniel, thanks for the answer. Probably I haven't expressed my problem in the right way. I have to generate a multicorrelated random processes starting from a target spectrum for each signal and a set of target coherence functions. The generated process doesn't follow the target coherence functions; for example, it isn't zero where I expect it to be, becouse it is affected by the coherence functions of the random noises used inside the AR method. So my problem is due to the non-zero coherence functions of the white noises.

[Daniel Shub]

Is your problem essentially that corrcoef(randn(1e3, 1), randn(1e3, 1)) doesn't return an identity matrix?

[Lapo]

The corrcoef matrix is near enought to the identity matrix. My problem is in

>>u=randn(Ns,2)

>>mscohere(u(:,1),u(:,2),[],[],Ns,'sample frequency')

I expect mscohere to be zero, but it always show a mean value 0.3. This affect the quality of the signal simulated by AR method. The same thing happen obviously with the cross-spectrum