Table of Z-Transforms for some standard signals

Signal Z-Transform

Region of Convergence (ROC)

\delta (n) 1 entire Z-plane
u[n] \frac{1}{1-z^{-1}} or\frac{z}{z-1} \left | z \right |> 1
u[-n-1] \frac{-1}{1-z^{-1}} or\frac{-z}{z-1} \left | z \right |< 1
a^{n}u[n] \frac{1}{1-az^{-1}} or\frac{z}{z-a} \left | z \right |> a
-a^{n}u[-n-1] \frac{1}{1-az^{-1}} or\frac{z}{z-a} \left | z \right |< a
na^{n}u[n] \frac{az^{-1}}{(1-az^{-1})^{2}} (or )\frac{az}{(z-a)^{2}} \left | z \right |> a
cos (\omega _{o}n)u[n] \frac{1-cos(\omega _{o})z^{-1}}{1-2cos(\omega _{o})z^{-1}+z^{-2}} \left | z \right |> 1
sin (\omega _{o}n)u[n] \frac{sin(\omega _{o})z^{-1}}{1-2cos(\omega _{o})z^{-1}+z^{-2}} \left | z \right |> 1
r^{n}cos (\omega _{o}n)u[n] \frac{1-rz^{-1}cos(\omega _{o})}{1-2rz^{-1}cos(\omega _{o})+z^{-2}r^{2}} \left | z \right |> \left | r \right |
r^{n}sin (\omega _{o}n)u[n] \frac{rz^{-1}sin(\omega _{o})}{1-2rz^{-1}cos(\omega _{o})+z^{-2}r^{2}} \left | z \right |> \left | r \right |
\frac{1}{n},n> 0 -\ln (1-z^{-1}) \left | z \right |> 1
a^{\left | n \right |} \forall n \frac{(1-a^{2})}{(1-az)(1-az^{-1})} \left | a \right |< \left | z \right |< \frac{1}{\left | a \right |}
-na^{n}u[-n-1] \frac{az^{-1}}{(1-az^{-1})^{2}} (or)\frac{az}{(z-a)^{2}} \left | z \right |> \left | a \right |
(n+1)a^{n}u[n] \frac{1}{(1-az^{-1})^{2}} (or)\frac{z^{2}}{(z-a)^{2}} \left | z \right |> \left | a \right |
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Author: Lakshmi Prasanna Ponnala

Completed M.Tech in Digital Electronics and Communication Systems and currently working as a faculty.