Referencia: Lathi Tabla 3.1 p285
\gamma_1 \neq \gamma_2No | x1[n] | x2[n] | x1[n]⊗x2[n] = x2[n]⊗x1[n] |
---|---|---|---|
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] |