1a.
w = 0:pi/500:pi;
H = 0.5 * (1+exp(-i*w));
plot(w, abs(H));
ylabel('magnitude');
xlabel('frequency');

1b.
w = 0:pi/500:pi;
H = 0.5 * (1+exp(-i*w));
plot(w, angle(H));
ylabel('phase');
xlabel('frequency');

2.

function result = CombFilter
w = [0:pi/2000:pi];
result  = 1 ./ (abs( 1-0.5*0.99*( exp(-i*w*40) - exp(-i*w*41)) ));
plot(w, result)



H = 1./(1 - 0.5*alpha*exp(-i*omega*N) - 0.5*alpha*exp(-i*omega*(N+1)));;



specgram(simout, 512, 8000)