11. Complex convolution theorem (or Multiplication in time domain) Let, $z\left\{x_{1}(n) ight\}=X_{1}(z) $ and $z\left\{x_{2}(n) ight\}=X_{2}(z)$. Now, the complex convolution theorem states that, $$ z\left\{x_{1}(n) x_{2}(n) ight\}=\frac{1}{2 \pi j} \oint_{C} X_{1}(v) X_{2}\left(\frac{z}{v} ight) v^{-1} d v $$ where, $v$ is a dummy variable used for contour integration. CS.JG.042