The White Gaussian Noise should contain a multivariate random numbers with three different realizations, each realization with mean 0 and variance 3,6,0.0012 respectively.
N=1000; % Input sample length
M = [0 0 0]; % Mean vector
var = [3 6 12*10^-4]; % Variance vector
Cov = var.*eye(3,3); % Covariance matrix
x = mvnrnd(M,Cov,N); % MultiVariate random vector added to the input
x1 = autocorr(x(:,1)); % Space Correlation of three realizations
x2 = autocorr(x(:,2));
x3 = autocorr(x(:,3));
Since time is a separate dimension, we get the Gaussian Random Variables by fixing a particular time instant(say t) in the Gaussian Random Process to obtain the above three realizations. So, we consider the time instants in such a way it satisfies the time step auto correlation function of the Gaussian Random Process.
