%Question #4
f=[0:5:4000];
f_0=2000;
f_s=8000;
w=2*pi*f/f_s;
z=exp(w*j);
B=500;

H=((0.16217*(z.*z-1))./(z.*z+0.67565));

figure
subplot(2,1,1), plot(f,abs(H))
title('Magnitude Response of H(z)')
ylabel('H(z)')
xlabel('f [Hz]')

subplot(2,1,2), plot(f,angle(H))
title('Phase Response of H(z)')
ylabel('Theta [rad]')
xlabel('f [Hz]')

%magnitude and phase @ f_0 
w=2*pi*f_0/f_s;
z=exp(w*j);
H=((0.16217*(z.*z-1))./(z.*z+0.67565));
mag_f_o=abs(H)
phase_f_0=angle(H)

%magnitude and phase @ f_0 +B/2
w=2*pi*(f_0+B/2)/f_s;
z=exp(w*j);
H=((0.16217*(z.*z-1))./(z.*z+0.67565));
mag=abs(H)
phase=angle(H)