} ചില സീ പരിവർത്തനജോടികൾ u : n ↦ u [ n ] = { 1 , n ≥ 0 0 , n 0 {\displaystyle u:n\mapsto u[n]={\begin{cases}1, n\geq 0\\0, n 0\end{cases}}} δ : n ↦ δ [ n ] = { 1 , n = 0 0 , n ≠ 0 {\displaystyle \delta :n\mapsto \delta [n]={\begin{cases}1, n=0\\0, n\neq 0\end{cases}}} സിഗ്നൽ , x [ n ] {\displaystyle x[n]} സീ പരിവർത്തനം, X ( z ) {\displaystyle X(z)} ഏകത്ര കേന്ദ്രീകരണ മേഖല 1 δ [ n ] {\displaystyle \delta [n]} 1 എല്ലായിടവും 2 δ [ n − n 0 ] {\displaystyle \delta [n-n_{0}]} z − n 0 {\displaystyle z^{-n_{0}}} z ≠ 0 {\displaystyle z\neq 0} 3 u [ n ] {\displaystyle u[n]\,} 1 1 − z − 1 {\displaystyle {\frac {1}{1-z^{-1}}}} | z | 1 {\displaystyle |z| 4 e − α n u [ n ] {\displaystyle e^{-\alpha n}u[n]} 1 1 − e − α z − 1 {\displaystyle 1 \over 1-e^{-\alpha }z^{-1}} | z | | e − α | {\displaystyle |z| 5 − u [ − n − 1 ] {\displaystyle -u[-n-1]} 1 1 − z − 1 {\displaystyle {\frac {1}{1-z^{-1}}}} | z | 1 {\displaystyle |z| 1} 6 n u [ n ] {\displaystyle nu[n]} z − 1 ( 1 − z − 1 ) 2 {\displaystyle {\frac {z^{-1}}{(1-z^{-1})^{2}}}} | z | 1 {\displaystyle |z| 7 − n u [ − n − 1 ] {\displaystyle -nu[-n-1]\,} z − 1 ( 1 − z − 1 ) 2 {\displaystyle {\frac {z^{-1}}{(1-z^{-1})^{2}}}} | z | 1 {\displaystyle |z| 1} 8 n 2 u [ n ] {\displaystyle n^{2}u[n]} z − 1 ( 1 + z − 1 ) ( 1 − z − 1 ) 3 {\displaystyle {\frac {z^{-1}(1+z^{-1})}{(1-z^{-1})^{3}}}} | z | 1 {\displaystyle |z| 9 − n 2 u [ − n − 1 ] {\displaystyle -n^{2}u[-n-1]\,} z − 1 ( 1 + z − 1 ) ( 1 − z − 1 ) 3 {\displaystyle {\frac {z^{-1}(1+z^{-1})}{(1-z^{-1})^{3}}}} | z | 1 {\displaystyle |z| 1\,} 10 n 3 u [ n ] {\displaystyle n^{3}u[n]} z − 1 ( 1 + 4 z − 1 + z − 2 ) ( 1 − z − 1 ) 4 {\displaystyle {\frac {z^{-1}(1+4z^{-1}+z^{-2})}{(1-z^{-1})^{4}}}} | z | 1 {\displaystyle |z| 11 − n 3 u [ − n − 1 ] {\displaystyle -n^{3}u[-n-1]} z − 1 ( 1 + 4 z − 1 + z − 2 ) ( 1 − z − 1 ) 4 {\displaystyle {\frac {z^{-1}(1+4z^{-1}+z^{-2})}{(1-z^{-1})^{4}}}} | z | 1 {\displaystyle |z| 1\,} 12 a n u [ n ] {\displaystyle a^{n}u[n]} 1 1 − a z − 1 {\displaystyle {\frac {1}{1-az^{-1}}}} | z | | a | {\displaystyle |z| 13 − a n u [ − n − 1 ] {\displaystyle -a^{n}u[-n-1]} 1 1 − a z − 1 {\displaystyle {\frac {1}{1-az^{-1}}}} | z | | a | {\displaystyle |z| |a|} 14 n a n u [ n ] {\displaystyle na^{n}u[n]} a z − 1 ( 1 − a z − 1 ) 2 {\displaystyle {\frac {az^{-1}}{(1-az^{-1})^{2}}}} | z | | a | {\displaystyle |z| 15 − n a n u [ − n − 1 ] {\displaystyle -na^{n}u[-n-1]} a z − 1 ( 1 − a z − 1 ) 2 {\displaystyle {\frac {az^{-1}}{(1-az^{-1})^{2}}}} | z | | a | {\displaystyle |z| |a|} 16 n 2 a n u [ n ] {\displaystyle n^{2}a^{n}u[n]} a z − 1 ( 1 + a z − 1 ) ( 1 − a z − 1 ) 3 {\displaystyle {\frac {az^{-1}(1+az^{-1})}{(1-az^{-1})^{3}}}} | z | | a | {\displaystyle |z| 17 − n 2 a n u [ − n − 1 ] {\displaystyle -n^{2}a^{n}u[-n-1]} a z − 1 ( 1 + a z − 1 ) ( 1 − a z − 1 ) 3 {\displaystyle {\frac {az^{-1}(1+az^{-1})}{(1-az^{-1})^{3}}}} | z | | a | {\displaystyle |z| |a|} 18 cos ⁡ ( ω 0 n ) u [ n ] {\displaystyle \cos(\omega _{0}n)u[n]} 1 − z − 1 cos ⁡ ( ω 0 ) 1 − 2 z − 1 cos ⁡ ( ω 0 ) + z − 2 {\displaystyle {\frac {1-z^{-1}\cos(\omega _{0})}{1-2z^{-1}\cos(\omega _{0})+z^{-2}}}} | z | 1 {\displaystyle |z| 19 sin ⁡ ( ω 0 n ) u [ n ] {\displaystyle \sin(\omega _{0}n)u[n]} z − 1 sin ⁡ ( ω 0 ) 1 − 2 z − 1 cos ⁡ ( ω 0 ) + z − 2 {\displaystyle {\frac {z^{-1}\sin(\omega _{0})}{1-2z^{-1}\cos(\omega _{0})+z^{-2}}}} | z | 1 {\displaystyle |z| 20 a n cos ⁡ ( ω 0 n ) u [ n ] {\displaystyle a^{n}\cos(\omega _{0}n)u[n]} 1 − a z − 1 cos ⁡ ( ω 0 ) 1 − 2 a z − 1 cos ⁡ ( ω 0 ) + a 2 z − 2 {\displaystyle {\frac {1-az^{-1}\cos(\omega _{0})}{1-2az^{-1}\cos(\omega _{0})+a^{2}z^{-2}}}} | z | | a | {\displaystyle |z| 21 a n sin ⁡ ( ω 0 n ) u [ n ] {\displaystyle a^{n}\sin(\omega _{0}n)u[n]} a z − 1 sin ⁡ ( ω 0 ) 1 − 2 a z − 1 cos ⁡ ( ω 0 ) + a 2 z − 2 {\displaystyle {\frac {az^{-1}\sin(\omega _{0})}{1-2az^{-1}\cos(\omega _{0})+a^{2}z^{-2}}}} | z | | a | {\displaystyle |z| ലാപ്ലേസ് പരിവർത്തനവുമ്മായുള്ളബന്ധം