(Solved):   Determine the impulse response and system function for causal LTI system \[ g_{t}+\frac{1} ...

 

Determine the impulse response and system function for causal LTI system \[ g_{t}+\frac{1}{2} g_{t-1}=\frac{1}{4}\left(f_{t}-f_{t-1}\right) \] where \( g_{t} \) is system output and \( f_{t} \) is system input. In addition, draw the zero-pole diagra and the amplitude response. Based on these, what can you say about the functioning of \( \mathrm{tl} \) system? ( 10 points)