An Observation

• The impulse response h_n of the filter is the output of the filter when the input is the signals $\{1 0 0 \ldots 0\}$.
• It is easily seen, that the impulse resonse equals the coefficients of the filter, i.e., $h_n=\frac{1}{N+1}$ for $n=0,\ldots,N$;
• Now, the Fourier transform of the impulse response is equal to the frequency response of the filter.
• This relationship relates the time-domain representation (impulse response) and the frequency-domain representation (frequency reponse).