In this problem we consider the effect of a single zero on the frequency response of a system. Let z = rej? be zero inside the unit circle (r

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H.(w) = 1 - re"e-jw = 1 -r cos(w - 0) + jr sin(w - e) (a) Show that the magnitude response is |H.(w) = [1- 2r cos(w - 6) + rj or, equivalently, 20 log10 1H:(w)| = 10log1o[1 - 2r cos(w - 6) + r²] (b) Show that the phase response is given as r sin(w - 6) 1- r costo - 6) 0. (w) = tan (c) Show that the group delay is given as P -r cos( - = (m). 1+r - 2r cos(w - 0) %3D (d) Plot the magnitude IH(w)id8. the phase O(w) and the group delay r,(@) for r = 0.7 and 8 = 0, 7/2. and r.