The impulse response of an FIR filter is h[n] = [n] + [n 1] + [n

The impulse response of an FIR filter is  h[n] = αδ[n] + βδ[n − 1] + αδ[n − 2], α > 0 and β > 0.

(a) Determine the value of α and β for which this filter has a dc gain |H(e^j0)|= 1, and linear phase ∠H(e^jω)= − ω.

(b) For the smallest possible β and the corresponding α obtained above  find the zeros of the filter, plot them in the Z-plane and indicate  their relation. Generalize the relation of the zeros for all possible  values of β and corresponding α, and find a general expression for  the two zeros.