# Matlab: How to implement expectation of product of hermitian matrix

I want to implement the following equation in Matlab:

$$\mathbf {R}_\mathbf {z}^a(\tilde{f}) = \mathbb {E} \left[\mathbf {z}(\tilde{f}) \mathbf {z}^H(\tilde{f}+a) \right]$$, $$\tilde{f} \in \left[0, f_s-a \right]$$

where $$\mathbf {z}(\tilde{f})$$ is a matrix, and $$a$$ takes values in the interval $$\left[0, f_s-a \right]$$. I am not sure how to implement the expectation operation, Is there some equivalent implementation in the time domain?

• I suppose the expectation is calculated over the distribution of random matrix $\mathbf{z}$? Because "the expected value of a random variable, intuitively, is the long-run average value of repetitions of the same experiment it represents", how about just generating, say $10^6$, realizations of $\mathbf{z}$ then averaging the corresponding $\mathbf{R}$? – AlexTP Feb 2 at 10:56
• @AlexTP, Pay attention that you are right under the assumption of Ergodicity of the random process. – Royi Feb 2 at 11:38
• @Royi totally argee ... – AlexTP Feb 2 at 13:33