# Convolución de Sumas – Tabla

Referencia: Lathi Tabla 3.1 p285

$\gamma_1 \neq \gamma_2$
 x1[n] x2[n] x1[n]⊗x2[n] = x2[n]⊗x1[n] No 1 δ[n-k] x[n] x[n-k] 2 $\gamma^{n} \mu[n]$ μ[n] $\frac{1-\gamma^{n+1}}{1-\gamma} \mu[n]$ 3 μ[n] μ[n] (n+1) μ[n] 4 $\gamma_1^{n} \mu[n]$ $\gamma_2^{n} \mu[n]$ $\frac{\gamma_1^{n+1} - \gamma_2^{n+1}}{\gamma_1 - \gamma_2} \mu[n]$ 5 $\gamma_1^{n} \mu[n]$ $\gamma_2^{n} \mu[-(n+1) ]$ $\frac{\gamma_1}{\gamma_2 - \gamma_1} \gamma_1^{n} \mu[n] +$ $+ \frac{\gamma_2}{\gamma_2 - \gamma_1} \gamma_2^{n} \mu[-(n+1)]$ $|\gamma_2| > |\gamma_1|$ 6 $n\gamma_1^{n} \mu[n]$ $\gamma_2^{n} \mu[n]$ $\frac{\gamma_1 \gamma_2}{(\gamma_1 - \gamma_2)^2} \Big[ \gamma_2^{n} - \gamma_1^{n} + \frac{\gamma_1 - \gamma_2}{\gamma_2}n \gamma_1^n \Big] \mu [n]$ $\gamma_1\neq \gamma_2$ 7 n μ[n] n μ[n] $\frac{1}{6} n (n-1) (n+1) \mu [n]$ 8 $\gamma^{n} \mu[n]$ $\gamma^{n} \mu[n]$ $(n+1) \gamma^{n} \mu[n]$ 9 $\gamma^{n} \mu[n]$ $n \mu[n]$ $\Big[ \frac{\gamma(\gamma^{n}-1)+n(1-\gamma)}{(1-\gamma)^2} \Big] \mu[n]$ 10 $|\gamma_1|^{n} \cos (\beta n + \theta) \mu [k]$ $|\gamma_2|^{n}\mu [n]$ $\frac{1}{R} \Big[ |\gamma_1|^{n+1} \cos [\beta (n+1) +\theta -\phi] -\gamma_2 ^{n+1} \cos (\theta - \phi) \Big] \mu[n]$ $R=\Big[|\gamma_1|^2 + \gamma_2^2 -2|\gamma_1|\gamma_2 \cos(\beta) \Big]^{\frac{1}{2}}$ $\phi = \tan ^{-1} \Big[ \frac{|\gamma_1| \sin(\beta)}{|\gamma_1| \cos (\beta) -\gamma_2} \Big]$ 11 $\mu [n]$ $n\mu [n]$ $\frac{n(n+1)}{2}\mu [n]$