Question

Convolution\nProblems 1) $x(n) = \alpha^n u(n)$ $\alpha \neq 1/3$ $or \{x(n) * h(n)\}$ $\{x(t) * h(t)\}$ $h(n) = \beta^n u(n)$ $|\alpha| \neq |\beta| < 1$ 2) $x(n) = h(n) = \alpha^n u(n)$ 3) $x(n) = (-\frac{1}{2})^n u(n-4)$ $h(n) = 4^n u(2-n)$ 4) $x(t) = e^{-\alpha t} u(t)$ $h(t) = e^{-\beta t} u(t)$ case 1 $\alpha \neq \beta$, case 2 $\alpha = \beta$ 5) $x(t) = (sin \pi t)[u(t) - u(t-2)]$ $h(t) = u(t-1) - u(t-3)$ $\overline{x(n) * h(n)} = \sum_{k=-\infty}^{\infty} x(k) h(n-k)$ $x(t) * h(t) = \int_{-\infty}^{\infty} x(\tau) h(t-\tau) d\tau$

          Convolution\nProblems
1) $x(n) = \alpha^n u(n)$
$\alpha \neq 1/3$
$or \{x(n) * h(n)\}$
$\{x(t) * h(t)\}$
$h(n) = \beta^n u(n)$
$|\alpha| \neq |\beta| < 1$
2) $x(n) = h(n) = \alpha^n u(n)$
3) $x(n) = (-\frac{1}{2})^n u(n-4)$
$h(n) = 4^n u(2-n)$
4) $x(t) = e^{-\alpha t} u(t)$  $h(t) = e^{-\beta t} u(t)$
case 1 $\alpha \neq \beta$, case 2 $\alpha = \beta$
5) $x(t) = (sin \pi t)[u(t) - u(t-2)]$
$h(t) = u(t-1) - u(t-3)$
$\overline{x(n) * h(n)} = \sum_{k=-\infty}^{\infty} x(k) h(n-k)$
$x(t) * h(t) = \int_{-\infty}^{\infty} x(\tau) h(t-\tau) d\tau$

$Convolution1) x(n) = α^n u(n) α≠ 1/3 or {x(n) * h(n)} {x(t) * h(t)} h(n) = β^n u(n) |α| ≠ |β| < 1 2) x(n) = h(n) = α^n u(n) 3) x(n) = (-(1)/(2))^n u(n-4) h(n) = 4^n u(2-n) 4) x(t) = e^-α t u(t) h(t) = e^-β t u(t) case 1 α≠β, case 2 α = β 5) x(t) = (sin π t)[u(t) - u(t-2)] h(t) = u(t-1) - u(t-3) x(n) * h(n) = ∑k=-∞^∞ x(k) h(n-k) x(t) * h(t) = ∫-∞^∞ x(τ) h(t-τ) dτ$

Added by Keith S.

Question

Please give Ace some feedback