Consider an FIR filter with the following filter coefficients: $b_0 = 4$, $b_1 = 8$, $b_2 = 4$. The input $x[n] = 6 \cos(\frac{\pi}{3}n + \frac{2\pi}{3})$ is applied to the system and the output $y[n] = A \cos(\omega n + \phi)$ is observed.
$\circ$ none of the above
$\circ$ $A = 16$
$\circ$ $\omega = \frac{\pi}{3}$
$\circ$ $\phi = \frac{2\pi}{3}$
$\circ$ $A = 48$
$\circ$ $\omega = \frac{\pi}{3}$
$\circ$ $\phi = \pi$
$\circ$ $A = 72$
$\circ$ $\omega = \frac{\pi}{3}$
$\circ$ $\phi = \frac{\pi}{3}$
