Transformada inversa de función en el dominio de X(z)
| X\left( z \right) | x\left[ n \right] |
| \frac{z}{z-a} | {{a}^{n}}u\left[ n \right] |
| \frac{z}{{{\left( z-a \right)}^{2}}} | n{{a}^{n}}u\left[ n \right] |
| \frac{z}{{{\left( z-a \right)}^{N+1}}} cuando N\textless 1 | \frac{n\left( n-1 \right)\ldots \left( n-N-1 \right)}{N!}{{a}^{\left( n-N \right)}} |
| \frac{z\left( C+jD \right)}{z-a{{e}^{j\text{ }\!\!\Omega\!\!\text{ }}}}+\frac{z\left( C-jD \right)}{z-a{{e}^{-j\text{ }\!\!\Omega\!\!\text{ }}}} | 2{{a}^{n}}\left[ C~cos\left( n\text{ }\!\!\Omega\!\!\text{ } \right)-D~sen\left( n\text{ }\!\!\Omega\!\!\text{ } \right) \right] |
| \frac{zK\angle \phi }{z-a{{e}^{j\text{ }\!\!\Omega\!\!\text{ }}}}+\frac{zK\angle -\phi }{z-a{{e}^{-j\text{ }\!\!\Omega\!\!\text{ }}}} | 2K{{a}^{n}}~cos\left( n\text{ }\!\!\Omega\!\!\text{ }+\phi \right) |
| \frac{z\left( C+jD \right)}{{{\left( z-a{{e}^{j\text{ }\!\!\Omega\!\!\text{ }}} \right)}^{2}}}+\frac{z\left( C-jD \right)}{{{(z-a{{e}^{-j\text{ }\!\!\Omega\!\!\text{ }}})}^{2}}} | 2n{{a}^{n-1}}\left[ C~cos\left[ \left( n-1 \right)\text{ }\!\!\Omega\!\!\text{ } \right]-D~sen\left[ \left( n-1 \right)\text{ }\!\!\Omega\!\!\text{ } \right] \right] |
| \frac{zK\angle \phi }{(z-a{{e}^{j\text{ }\!\!\Omega\!\!\text{ })}}^{2}}+\frac{zK\angle -\phi }{{{\left( z-a{{e}^{-j\text{ }\!\!\Omega\!\!\text{ }}} \right)}^{2}}} | 2Kn{{a}^{n-1}}~cos\left( \left( n-1 \right)\text{ }\!\!\Omega\!\!\text{ }+\phi \right) |
| \frac{zK\angle \phi }{(z-a{{e}^{j\text{ }\!\!\Omega\!\!\text{ })}}^{N+1}}+\frac{zK\angle -\phi }{{{\left( z-a{{e}^{-j\text{ }\!\!\Omega\!\!\text{ }}} \right)}^{N+1}}} | 2K\frac{n\left( n-1 \right)\ldots \left( n-N-1 \right)}{N!}{{a}^{n-N}}~ cos\left( \left( n-N \right)\text{ }\!\!\Omega\!\!\text{ }+\phi \right) |