FIR Filtering

An FIR filter is defined by the input-output relationship

y[n] = x[n] - 2x[n-1] + x[n-2].

1.

Compute the output y[n] if the input is $x[n]=\{2,4,6,4,2\}$.

2.

Compute the output y[n] if the input is the unit-step sequence u[n].

3.

Without computing the frequency response, explain if the FIR filter considered in this problem is a low-pass or a high-pass filter.

Reminder: The unit-step sequence is defined as

$$u[n] = \left\{ \begin{array}{cl} 0 & \mbox{for $n<0$ }\\ 1 & \mbox{for $n \geq 1$ } \end{array} \right.$$