A discrete-time system with input u and output y has transfer function
G(z) = \frac{Y(z)}{U(z)} = \frac{1+z^{-1}}{4-4z^{-1}+z^{-2}}.
Which of the following difference equations represent the time-domain relationship between u and y for this system?

Question

A discrete-time system with input   u  and output   y  has transfer function 
   G(z) = \frac{Y(z)}{U(z)} = \frac{1+z^{-1}}{4-4z^{-1}+z^{-2}}. 
 Which of the following difference equations represent the time-domain relationship between   u  and   y  for this system?

Answer

4u[k] - 4u[k-1]+u[k-2] = y[k]+y[k-1]  for all   k

Answer

4y[k] - 4y[k-1]+y[k-2] = u[k]  for all   k

Answer

4y[k] - 4y[k-1]+y[k-2] = u[k]+u[k-1]  for all   k

Answer

4u[k] - 4u[k-1]+u[k-2] = y[k]  for all   k

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