# Translations:Z-transform/30/en

${\displaystyle u_{n}=1\;{\text{for}}\;k\geq \;0}$ | ${\displaystyle {\frac {1}{1-Z}}}$ | ${\displaystyle |z|\;<1}$ |- | Negative anticausal step | ${\displaystyle -u_{-n-1}}$ | ${\displaystyle {\frac {1}{1-Z}}}$ | ${\displaystyle |z|\;>1}$ |- | Ramp | ${\displaystyle nu_{n}}$ | ${\displaystyle {\frac {Z}{(1-Z)^{2}}}}$ | ${\displaystyle |Z|\;<\;1}$ |- | Causal geometric | ${\displaystyle \alpha ^{n}u_{n}}$ | ${\displaystyle {\frac {1}{1-\alpha Z}}}$ | ${\displaystyle |Z|\;<\;\alpha }$ |- | Negative anticausal geometric | ${\displaystyle -\alpha ^{n}u_{-n-1}}$ | ${\displaystyle {\frac {1}{1-\alpha Z}}}$ | ${\displaystyle |Z|\;>\;\alpha }$ |- | Causal cosine | ${\displaystyle u_{n}\cos(\theta n)}$ | ${\displaystyle {\frac {1-\cos \theta \;Z}{1-2\;\cos \theta \;Z+Z^{2}}}}$ | ${\displaystyle |Z|\;<1}$ |- | Causal sine | ${\displaystyle u_{n}\sin(\theta n)}$ | ${\displaystyle {\frac {Z\;\sin \theta }{1-2\;\cos \theta \;Z+Z^{2}}}}$ | ${\displaystyle |Z|\;<1}$ |- | Causal geometric cosine | ${\displaystyle u_{n}\alpha ^{n}\cos(\theta n)}$ | ${\displaystyle {\frac {Z(1-\alpha \cos \theta \;Z)}{\alpha ^{2}-2\alpha \;\cos \theta \;Z+Z^{2}}}}$ | ${\displaystyle |Z|\;<\;|\alpha |}$ |- | Causal geometric sine | ${\displaystyle u_{n}\alpha ^{n}\sin(\theta n)}$ | ${\displaystyle {\frac {Z\alpha \;\sin \theta }{\alpha ^{2}-2\alpha \cos \theta \;Z+Z^{2}}}}$ | ${\displaystyle |Z|\;<\;|\alpha |}$ |}