Initial Value Theorem

Let x(n) be a signal causal, and let X(Z) be its Z-Transform. Then :

\(X(z)= \sum_{n=-\infty}^{+\infty }x(n)Z^{-n} \quad\)

\(X\left(Z\right)=x\left(0\right)+x\left(1\right)Z^{-1}+x\left(2\right)Z^{-2}+\ldots\)

\(X(0)=\lim\limits_{Z \to +\infty} X(Z) \quad (15)\)