Suppose a zero-mean Gaussian random process,X(t) , has a PSD given by

 We desire to simulate a 5-ms segment of this process sampled at a rate of 2 kHz. Therefore, 10 samples will need to be created in our simulation. We will create the samples of the process by first generating 10 uncorrelated Gaussian random variables and then pass those variables through an appropriate transformation matrix, .

(a) Find the correlation matrix of the 10 samples.

(b) Find the form of the matrix that will produce samples with the desired correlation matrix.