# Table of Z-Transforms for some standard signals

 Signal Z-Transform Region of Convergence (ROC) $\delta&space;(n)$$\delta&space;(n)$ $1$$1$ entire Z-plane $u[n]$$u[n]$ $\frac{1}{1-z^{-1}}&space;or\frac{z}{z-1}$$\frac{1}{1-z^{-1}}&space;or\frac{z}{z-1}$ $\left&space;|&space;z&space;\right&space;|>&space;1$$\left&space;|&space;z&space;\right&space;|>&space;1$ $u[-n-1]$$u[-n-1]$ $\frac{-1}{1-z^{-1}}&space;or\frac{-z}{z-1}$$\frac{-1}{1-z^{-1}}&space;or\frac{-z}{z-1}$ $\left&space;|&space;z&space;\right&space;|<&space;1$$\left&space;|&space;z&space;\right&space;|<&space;1$ $a^{n}u[n]$$a^{n}u[n]$ $\frac{1}{1-az^{-1}}&space;or\frac{z}{z-a}$$\frac{1}{1-az^{-1}}&space;or\frac{z}{z-a}$ $\left&space;|&space;z&space;\right&space;|>&space;a$$\left&space;|&space;z&space;\right&space;|>&space;a$ $-a^{n}u[-n-1]$$-a^{n}u[-n-1]$ $\frac{1}{1-az^{-1}}&space;or\frac{z}{z-a}$$\frac{1}{1-az^{-1}}&space;or\frac{z}{z-a}$ $\left&space;|&space;z&space;\right&space;|<&space;a$$\left&space;|&space;z&space;\right&space;|<&space;a$ $na^{n}u[n]$$na^{n}u[n]$ $\frac{az^{-1}}{(1-az^{-1})^{2}}&space;(or&space;)\frac{az}{(z-a)^{2}}$$\frac{az^{-1}}{(1-az^{-1})^{2}}&space;(or&space;)\frac{az}{(z-a)^{2}}$ $\left&space;|&space;z&space;\right&space;|>&space;a$$\left&space;|&space;z&space;\right&space;|>&space;a$ $cos&space;(\omega&space;_{o}n)u[n]$$cos&space;(\omega&space;_{o}n)u[n]$ $\frac{1-cos(\omega&space;_{o})z^{-1}}{1-2cos(\omega&space;_{o})z^{-1}+z^{-2}}$$\frac{1-cos(\omega&space;_{o})z^{-1}}{1-2cos(\omega&space;_{o})z^{-1}+z^{-2}}$ $\left&space;|&space;z&space;\right&space;|>&space;1$$\left&space;|&space;z&space;\right&space;|>&space;1$ $sin&space;(\omega&space;_{o}n)u[n]$$sin&space;(\omega&space;_{o}n)u[n]$ $\frac{sin(\omega&space;_{o})z^{-1}}{1-2cos(\omega&space;_{o})z^{-1}+z^{-2}}$$\frac{sin(\omega&space;_{o})z^{-1}}{1-2cos(\omega&space;_{o})z^{-1}+z^{-2}}$ $\left&space;|&space;z&space;\right&space;|>&space;1$$\left&space;|&space;z&space;\right&space;|>&space;1$ $r^{n}cos&space;(\omega&space;_{o}n)u[n]$$r^{n}cos&space;(\omega&space;_{o}n)u[n]$ $\frac{1-rz^{-1}cos(\omega&space;_{o})}{1-2rz^{-1}cos(\omega&space;_{o})+z^{-2}r^{2}}$$\frac{1-rz^{-1}cos(\omega&space;_{o})}{1-2rz^{-1}cos(\omega&space;_{o})+z^{-2}r^{2}}$ $\left&space;|&space;z&space;\right&space;|>&space;\left&space;|&space;r&space;\right&space;|$$\left&space;|&space;z&space;\right&space;|>&space;\left&space;|&space;r&space;\right&space;|$ $r^{n}sin&space;(\omega&space;_{o}n)u[n]$$r^{n}sin&space;(\omega&space;_{o}n)u[n]$ $\frac{rz^{-1}sin(\omega&space;_{o})}{1-2rz^{-1}cos(\omega&space;_{o})+z^{-2}r^{2}}$$\frac{rz^{-1}sin(\omega&space;_{o})}{1-2rz^{-1}cos(\omega&space;_{o})+z^{-2}r^{2}}$ $\left&space;|&space;z&space;\right&space;|>&space;\left&space;|&space;r&space;\right&space;|$$\left&space;|&space;z&space;\right&space;|>&space;\left&space;|&space;r&space;\right&space;|$ $\frac{1}{n},n>&space;0$$\frac{1}{n},n>&space;0$ $-\ln&space;(1-z^{-1})$$-\ln&space;(1-z^{-1})$ $\left&space;|&space;z&space;\right&space;|>&space;1$$\left&space;|&space;z&space;\right&space;|>&space;1$ $a^{\left&space;|&space;n&space;\right&space;|}&space;\forall&space;n$$a^{\left&space;|&space;n&space;\right&space;|}&space;\forall&space;n$ $\frac{(1-a^{2})}{(1-az)(1-az^{-1})}$$\frac{(1-a^{2})}{(1-az)(1-az^{-1})}$ $\left&space;|&space;a&space;\right&space;|<&space;\left&space;|&space;z&space;\right&space;|<&space;\frac{1}{\left&space;|&space;a&space;\right&space;|}$$\left&space;|&space;a&space;\right&space;|<&space;\left&space;|&space;z&space;\right&space;|<&space;\frac{1}{\left&space;|&space;a&space;\right&space;|}$ $-na^{n}u[-n-1]$$-na^{n}u[-n-1]$ $\frac{az^{-1}}{(1-az^{-1})^{2}}&space;(or)\frac{az}{(z-a)^{2}}$$\frac{az^{-1}}{(1-az^{-1})^{2}}&space;(or)\frac{az}{(z-a)^{2}}$ $\left&space;|&space;z&space;\right&space;|>&space;\left&space;|&space;a&space;\right&space;|$$\left&space;|&space;z&space;\right&space;|>&space;\left&space;|&space;a&space;\right&space;|$ $(n+1)a^{n}u[n]$$(n+1)a^{n}u[n]$ $\frac{1}{(1-az^{-1})^{2}}&space;(or)\frac{z^{2}}{(z-a)^{2}}$$\frac{1}{(1-az^{-1})^{2}}&space;(or)\frac{z^{2}}{(z-a)^{2}}$ $\left&space;|&space;z&space;\right&space;|>&space;\left&space;|&space;a&space;\right&space;|$$\left&space;|&space;z&space;\right&space;|>&space;\left&space;|&space;a&space;\right&space;|$
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