Table of Z-Transforms#

	f[n]	F(z).	Region of Convergence
1.	${\displaystyle \delta [n]}$	${\displaystyle 1}$
2	${\displaystyle \delta [n-m]}$	${\displaystyle z^{-m}}$
3	${\displaystyle a^n{u}_0[n]}$	${\displaystyle \frac{z}{z-a}}$	$\mid z\mid >a$
4	${\displaystyle u_0[n]}$	${\displaystyle \frac{z}{z-1}}$	$\mid z\mid >1$
5	${\displaystyle (e^{-an{T}_s})u_0[n]}$	${\displaystyle \frac{z}{z-e^{-a{T}_s}}}$	${\displaystyle \mid e^{-a{T}_s}{z}^{-1}\mid <1}$
6	${\displaystyle (\cos na{T}_s)u_0[n]}$	${\displaystyle \frac{z^2-z\cos a{T}_s}{z^2-2z\cos a{T}_s+1}}$	$\mid z\mid >1$
7	${\displaystyle (\sin na{T}_s)u_0[n]}$	${\displaystyle \frac{z\sin a{T}_s}{z^2-2z\cos a{T}_s+1}}$	$\mid z\mid >1$
8	${\displaystyle (a^n\cos na{T}_s)u_0[n]}$	${\displaystyle \frac{z^2-az\cos a{T}_s}{z^2-2az\cos a{T}_s+a^2}}$	$\mid z\mid >1$
9	${\displaystyle (a^n\sin na{T}_s)u_0[n]}$	${\displaystyle \frac{az\sin a{T}_s}{z^2-2az\cos a{T}_s+a^2}}$	$\mid z\mid >1$
10	${\displaystyle u_0[n]-u_0[n-m]}$	${\displaystyle \frac{z^m-1}{z^{m-1}(z-1)}}$
11	${\displaystyle n{u}_0[n]}$	${\displaystyle \frac{z}{(z-1{)}^2}}$
12	${\displaystyle n^2{u}_0[n]}$	${\displaystyle \frac{z(z+1)}{(z-1{)}^3}}$
13	${\displaystyle [n+1]u_0[n]}$	${\displaystyle \frac{z^2}{(z-1{)}^2}}$
14	${\displaystyle a^{n}n{u}_0[n]}$	${\displaystyle \frac{az}{(z-a{)}^2}}$
15	${\displaystyle a^n{n}^2{u}_0[n]}$	${\displaystyle \frac{az(z+a)}{(z-a{)}^3}}$
16	${\displaystyle a^{n}n[n+1]u_0[n]}$	${\displaystyle \frac{2a{z}^2}{(z-a{)}^3}}$

See also: Wikibooks: Engineering_Tables/Z_Transform_Table and Z-Transform—WolframMathworld for more complete references.