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?

  • $\begingroup$ 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 $\mathbf{R}$? $\endgroup$ – AlexTP Feb 2 '19 at 10:56
  • 1
    $\begingroup$ @AlexTP, Pay attention that you are right under the assumption of Ergodicity of the random process. $\endgroup$ – Royi Feb 2 '19 at 11:38
  • $\begingroup$ @Royi totally argee ... $\endgroup$ – AlexTP Feb 2 '19 at 13:33

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