In this topic, you study the Table of inverse Z-Transform.
Definition: Z-transform of discrete time signal $x[n]$ is
\[X[z] = \sum\limits_{n = – \infty }^\infty {x[n]} {z^{ – n}}\]
Using above property, the Z-transform of Basic Functions are
| Discrete time signal x[n] | Z-transform X[z] | Region of convergence (ROC) |
| \[\delta [n] \] | \[1\] | \[|z| > 1\] |
| \[{a^n}u[n] \] | \[\frac{{a{z^{ – 1}}}}{{{{(1 – {z^{ – 1}})}^2}}}\] | \[|z| > |a|\] |
| \[ – n{a^n}u[ – n – 1] \] | \[\frac{{a{z^{ – 1}}}}{{{{(1 – {z^{ – 1}})}^2}}}\] | \[|z| < |a|\] |
| \[u[n] \] | \[\frac{1}{{1 – {z^{ – 1}}}}\] | \[|z| > 1\] |
| \[-u[-n-1] \] | \[\frac{1}{{1 – {z^{ – 1}}}}\] | \[|z| < 1\] |
| \[\sin ({\omega _o}n)u[n]\] | \[\frac{{z.\sin {\omega _o}}}{{{z^2} – 2z\cos {\omega _o} + 1}}\] | \[|z| > 1\] |
| \[\cos ({\omega _o}n)u[n]\] | \[\frac{{z(z – \cos {\omega _o})}}{{{z^2} – 2z\cos {\omega _o} + 1}}\] | \[|z| > 1\] |