The 8-point running-sum filter is an FIR filter with coefficients {bk} = {1, 1, 1, 1, 1, 1, 1, 1,}.
(a) Use FFT spectrum analysis to plot the frequency response of the 8-pt. running-sum filter.
(b) Suppose that the input to the 8-pt. running-sum filter is x[n] whose DTFT has nonzero components only at ώ1 = 0.25π, ω2 = 0.5π, and a DC value of X0 = 3. Explain why the output of the 8-pt. running-sum filter is then y[n] = 24 for all n. Use values from the plot of |H(ejω)| versus ω to support your explanation.
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