Inverse Z-Transform Table

In this topic, you study the Table of Z-Transform.

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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)
\[1\]	\[\delta [n] \]	\[|z| > 1\]
\[\frac{{a{z^{ – 1}}}}{{{{(1 – {z^{ – 1}})}^2}}}\]	\[{a^n}u[n] \]	\[|z| > |a|\]
\[\frac{{a{z^{ – 1}}}}{{{{(1 – {z^{ – 1}})}^2}}}\]	\[ – n{a^n}u[ – n – 1] \]	\[|z| < |a|\]
\[\frac{1}{{1 – {z^{ – 1}}}}\]	\[u[n] \]	\[|z| > 1\]
\[\frac{1}{{1 – {z^{ – 1}}}}\]	\[-u[-n-1] \]	\[|z| < 1\]
\[\frac{{z.\sin {\omega _o}}}{{{z^2} – 2z\cos {\omega _o} + 1}}\]	\[\sin ({\omega _o}n)u[n]\]	\[|z| > 1\]
\[\frac{{z(z – \cos {\omega _o})}}{{{z^2} – 2z\cos {\omega _o} + 1}}\]	\[\cos ({\omega _o}n)u[n]\]	\[|z| > 1\]