The 8-point running-sum filter is an FIR filter with coefficients { } = (1, 1, 1, 1, 1, 1, 1, 1…

The 8-point running-sum filter is an FIR filter with coefficients {} = (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 DIET has nonzero components only at  = 0.25π,  = 0.5π and  = 0.75π, and a DC value of  = 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  versus  to support your explanation.

 

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