Solution to Q4 of Week 14 Quiz Pool
Conducting 2D Z transform on both sides of the equation and using time shifting property we get
$ Y(z_1,z_2)=X(z_1,z_2)+\frac{1}{2}\frac{z_1}{z_2}Y(z_1,z_2) $
where $ Y(z_1,z_2) $ is the 2D Z transform of y[m,n] and $ X(z_1,z_2) $ is the 2D Z transform of x[m,n]
Then $ H(z_1 ,z_2)=\frac{Y(z_1 ,z_2)}{X(z_1 ,z_2)}=\frac{2z_2}{2z_2-z_1} $
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