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b = [1 1 1 1];
a = [1 0 0 0];
[H, w] = freqz(b, a, linspace(-2*pi, 2*pi, 1000));
%freqz(b, a, 'whole')
%title('H(e^{j\omega})');
plot(w/pi, abs(H));
xlabel('\omega/\pi');
ylabel('|H(e^{j\omega})|');

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A = 2*(cos(1.5*w)+cos(0.5*w));    % Note that period of A is 4*pi, not 2*pi!
plot(w/pi, A);
xlabel('\omega/\pi');
ylabel('A(e^{j\omega})');

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plot(w/pi, (angle(H))/pi);
xlabel('\omega/\pi');
ylabel('\angle H(e^{j\omega})');

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Psi = -1.5*w;
plot(w/pi, Psi/pi);
xlabel('\omega/\pi');
ylabel('\Psi(e^{j\omega})');

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