How to simulate a channel using Jake’s model

This is only a latex test.

$s(t)=Re\left\{u(t) e^{j 2 \pi f_{c} t}\right\}=Re\{u(t)\} \cos \left(2 \pi f_{c} t\right)-Im\{u(t)\} \sin \left(2 \pi f_{c} t\right)$

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