Referencia: Lathi Tabla 5.1 Transformada z p492. Oppenheim tabla 10.2 p776, Schaum Hsu Tabla 4-1 p170.
| No. | x[n] | X[z] | ROC | |
|---|---|---|---|---|
| 1a | δ[n] | 1 | Toda z | |
| 1b | δ[n-m] | z-m | Toda z excepto 0 (si m>0) ó ∞ (si m<0) |
|
| 2a | μ[n] | \frac{z}{z-1} | \frac{1}{1-z^{-1}} | |z|>1 |
| 2b | -μ[-n-1] | \frac{z}{z-1} | \frac{1}{1-z^{-1}} | |z|<1 |
| 3 | n μ[n] | \frac{z}{(z-1)^2} | \frac{z^{-1}}{(1- z^{-1})^2} | |z|>1 |
| 4 | n2 μ[n] | \frac{z(z+1)}{(z-1)^3} | ||
| 5 | n3 μ[n] | \frac{z(z^2 + 4z + 1)}{(z-1)^4} | ||
| 6a | γn μ[n] | \frac{z}{z-\gamma} | \frac{1}{1-\gamma z^{-1}} | |z|>|γ| |
| 6b | -γn μ[-n-1] | \frac{z}{z-\gamma} | \frac{1}{1-\gamma z^{-1}} | |z|<|γ| |
| 7 | γn-1 μ[n-1] | \frac{1}{z-\gamma} | ||
| 8a | n γn μ[n] | \frac{\gamma z}{(z-\gamma)^2} | \frac{\gamma z^{-1}}{(1- \gamma z^{-1})^2} | |z|>|γ| |
| 8b | -n γn μ[-n-1] | \frac{\gamma z}{(z-\gamma)^2} | \frac{\gamma z^{-1}}{(1- \gamma z^{-1})^2} | |z|<|γ| |
| 8c | (n+1) γn μ[n] | \Big[ \frac{z}{z-\gamma}\Big]^2 | \frac{1}{(1- \gamma z^{-1})^2} | |z|>|γ| |
| 9 | n2 γn μ[n] | \frac{\gamma z (z + \gamma)}{(z - \gamma)^3 } | ||
| 10 | \frac{n(n-1)(n-2) \text{...} (n-m+1)}{\gamma^m m!}\gamma^n \mu[n] | \frac{ z}{(z-\gamma)^{m+1}} | ||
| 11a | |γ|n cos(βn) μ[n] | \frac{ z \big(z-|\gamma | \cos (\beta ) \big)}{z^2-(2|\gamma | \cos (\beta ))z +|\gamma |^2} | |z|>γ | |
| 11b | |γ|n sin(βn) μ[n] | \frac{ z |\gamma | \sin (\beta )}{z^2-(2|\gamma | \cos (\beta ))z +|\gamma |^2} | |z|>γ | |
| 12a | r|γ|n cos(βn+θ) μ[n] | \frac{ rz[z \cos (\theta) - |\gamma | \cos (\beta -\theta)]}{z^2-(2|\gamma | \cos (\beta ))z +|\gamma |^2} | ||
| 12b | r|γ|n cos(βn+θ) μ[n] γ = |γ| ejβ |
\frac{\big(0.5r e^{j \theta} \big)z}{z - \gamma} + \frac{\big(0.5r e^{-j \theta} \big)z}{z - \gamma^{*}} | ||
| 12c | r|γ|n cos(βn+θ) μ[n] | \frac{z(Az +B)}{z^2 + 2az + |\gamma|2} | ||
| r = \sqrt{\frac{A^2|\gamma |^2 + B^2 - 2AaB}{|\gamma |^2 - a^2}} | \beta = \cos ^{-1} \frac{-a}{|\gamma |}
\theta = tan^{-1} \frac{ Aa - B}{A \sqrt{|\gamma |^2 - a^2}} |
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| 13 | {an ; 0≤ n ≤ N-1 {0 ; otro caso |
\frac{1-a^N z^{-n}}{1-az^{-1}} | |z|>0 | |