In this topic, you study the Table of Z-Transform.
Definition: The inverse Z-transform of X[z] is
{x_n} = \frac{1}{{2\pi j}}\oint\limits_C {X[z]{z^{n – 1}}dz}
Using above property, the inverse Z-transform of Basic Functions are
| X[z] | x(n) | Region of convergence (ROC) |
| 1 | \delta [n] | |z| > 1 |
| \frac{{a{z^{ – 1}}}}{{{{(1 – {z^{ – 1}})}^2}}} | {a^n}u[n] | |z| > |a| |
| \frac{{a{z^{ – 1}}}}{{{{(1 – {z^{ – 1}})}^2}}} | – n{a^n}u[ – n – 1] | |z| < |a| |
| \frac{1}{{1 – {z^{ – 1}}}} | u[n] | |z| > 1 |
| \frac{1}{{1 – {z^{ – 1}}}} | -u[-n-1] | |z| < 1 |
| \frac{{z.\sin {\omega _o}}}{{{z^2} – 2z\cos {\omega _o} + 1}} | \sin ({\omega _o}n)u[n] | |z| > 1 |
| \frac{{z(z – \cos {\omega _o})}}{{{z^2} – 2z\cos {\omega _o} + 1}} | \cos ({\omega _o}n)u[n] | |z| > 1 |