Example: Given $x(n)= \delta(n)+ 2\cdot \delta(n-1)- \delta(n-3)$ and $h(n)=2\cdot \delta(n+1) + 2\cdot \delta(n-1)$ z transforms of $x(n)$ and $h(n)$ are $X(Z)= 1 + 2\cdot z^{-1} - z^{-3}$ $H(Z) = 2 \cdot z^{1} + 2 \cdot z^{-1}$ convolution in time domain leads to multiplication in z transform $x(n) \ast h(n) = X(Z) \cdot Y(Z)$ $Y(Z)= X(Z) \cdot H(Z)= 2\cdot z + 4+ 2\cdot z^{-1}+2\cdot z^{-2} -2\cdot z^{-4} $ taking inverse z transform $y(n)= 2\delta(n+1) + 4 \delta + 2 \delta(n-1) + 4 \delta(n-2)-2\delta(n-4)$