I am trying to understand Section 2.2.3 of the book "Fundamentals of wireless communication" by Tse and Viswanath. In this section the authors explain how to go from the continuous time baseband model to the discrete time baseband model. An image of the relevant pages are given below.

I am going to use equation numbers from the book. My question is the following:

If one looks at equation 2.29 it shows the sampling theorem. If I understand correctly that summation is the Whittaker–Shannon interpolation formula and it is from $-\infty$ to $\infty$.

This means in equation (2.33) the variable $\ell$ is from $-\infty$ to $\infty$. And this will imply the same in equation (2.35).

Does this not make the system non causal? Because if the variable $\ell$ is allowed to be negative, the output sample at zero can depend on any future input samples.

May be I am missing something on why the variable $\ell$ is not allowed to go negative, can someone clarify?

Tse Book relevant pages



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