function X = dtft ( x , n , w )
    % DTFT Computes Discrete-time Fourier transform
    % @param x : finite duration sequence (vector) over n
    % @param n : sample indices vector
    % @param w : frequency vector
    % @return X : DTFT of x[n] at frequencies w
    % this function does not use for loops
    X = sum(x(:) .* exp(-1j * n(:) * w), 1);
end

n = -10:10;
x = (0.8) .^ abs(n) .* ((n >= -10) & (n < 11));
w = linspace(-pi, pi, 1000);

X = dtft(x, n, w);

magnitude = abs(X);
phase = angle(X);
figure;
subplot(2, 1, 1);
plot(w, magnitude);
title('Magnitude Response');
xlabel('Frequency (rad/sample)');
ylabel('|X(w)|');
subplot(2, 1, 2);
plot(w, phase);
title('Phase Response');
xlabel('Frequency (rad/sample)');
ylabel('Phase(rad)');