Frequency Response of FIR Filters

Throughout this problem consider the length-four moving average FIR filter

$$y[n] = \frac{1}{4} \sum_{k=0}^3 x[n-k].$$

1.

Compute the output of this filter if the input is $x[n]=\exp(j 2 \pi 0 n)$.

2.

Compute the output of this filter if the input is $x[n]=\exp(j 2 \pi \frac{1}{2} n)$.

3.

Compute the frequency response of this filter. Determine the magnitude response and the phase response.

4.

Explain, what information about the filter is provided by the frequency response.

5.

What is the output of the filter if the input signal is $x[n]=\{\ldots \; 2 \; 0 \; 2 \; 0 \; 2 \; 0 \ldots\}$?