Engineering Tables/Z Transform Table

Here:

• $u[n]=1$ for $n>=0$, $u[n]=0$ for $n<0$
• $\delta[n] = 1$ for $n=0$, $\delta[n] = 0$ otherwise

	Signal, $x[n]$	Z-transform, $X(z)$	ROC
1	$\delta[n] \,$	$1\,$	$\mbox{all }z\,$
2	$\delta[n-n_0] \,$	$z^{-n_0} \,$	$z \neq 0\,$
3	$u[n] \,$	$\frac{1}{1-z^{-1} }$	$|z| > 1\,$
4	$- u[-n-1] \,$	$\frac{1}{1 - z^{-1}}$	$|z| < 1\,$
5	$n u[n] \,$	$\frac{z^{-1}}{( 1-z^{-1} )^2}$	$|z| > 1\,$
6	$- n u[-n-1] \,$	$\frac{z^{-1} }{ (1 - z^{-1})^2 }$	$|z| < 1 \,$
7	$n^2 u[n] \,$	$\frac{ z^{-1} (1 + z^{-1} )}{(1 - z^{-1})^3}$	$|z| > 1\,$
8	$- n^2 u[-n - 1] \,$	$\frac{ z^{-1} (1 + z^{-1} )}{(1 - z^{-1})^3}$	$|z| < 1\,$
9	$n^3 u[n] \,$	$\frac{z^{-1} (1 + 4 z^{-1} + z^{-2} )}{(1-z^{-1})^4}$	$|z| > 1\,$
10	$- n^3 u[-n -1] \,$	$\frac{z^{-1} (1 + 4 z^{-1} + z^{-2} )}{(1-z^{-1})^4}$	$|z| < 1\,$
11	$a^n u[n] \,$	$\frac{1}{1-a z^{-1}}$	$|z| > |a|\,$
12	$-a^n u[-n-1] \,$	$\frac{1}{1-a z^{-1}}$	$|z| < |a|\,$
13	$n a^n u[n] \,$	$\frac{az^{-1} }{ (1-a z^{-1})^2 }$	$|z| > |a|\,$
14	$-n a^n u[-n-1] \,$	$\frac{az^{-1} }{ (1-a z^{-1})^2 }$	$|z| < |a|\,$
15	$n^2 a^n u[n] \,$	$\frac{a z^{-1} (1 + a z^{-1}) }{(1-a z^{-1})^3}$	$|z| > |a|\,$
16	$- n^2 a^n u[-n -1] \,$	$\frac{a z^{-1} (1 + a z^{-1}) }{(1-a z^{-1})^3}$	$|z| < |a|\,$
17	$\cos(\omega_0 n) u[n] \,$	$\frac{ 1-z^{-1} \cos(\omega_0) }{ 1-2z^{-1}\cos(\omega_0)+ z^{-2} }$	$|z| >1\,$
18	$\sin(\omega_0 n) u[n] \,$	$\frac{ z^{-1} \sin(\omega_0) }{ 1-2z^{-1}\cos(\omega_0)+ z^{-2} }$	$|z| >1\,$
19	$a^n \cos(\omega_0 n) u[n] \,$	$\frac{ 1-a z^{-1} \cos( \omega_0) }{ 1-2az^{-1}\cos(\omega_0)+ a^2 z^{-2} }$	$|z| > |a|\,$
20	$a^n \sin(\omega_0 n) u[n] \,$	$\frac{ az^{-1} \sin(\omega_0) }{ 1-2az^{-1}\cos(\omega_0)+ a^2 z^{-2} }$	$|z| > |a|\,$