DEFINITION of z-transform is GIVEN by,\(X\left( z \right) = \mathop \sum \limits_{n = - \infty }^\infty x\left( n \right){z^{ - n}}\) Calculation:Given signal, x(n) = an U(n)The z-transform of the above-given signal is given by\(X\left( z \right) = \mathop \sum \limits_{n = - \infty }^\infty x\left( n \right){z^{ - n}}\)\(X\left( z \right) = \mathop \sum \limits_{n = 0}^\infty {a^n}{z^{ - n}}\)\( = \mathop \sum \limits_{n = 0}^\infty {\left( {a{z^{ - 1}}} \right)^n}\)\(=\FRAC{z}{{z - \alpha }}\)Note: The z-transform of x(n) = -an u(-n – 1) is given by\( = \frac{1}{{1 - a{z^{ - 1}}}} = \frac{z}{{z - a}};ROC:\left| z \right| < \left| a \right|\)