fft magnitude and phase (Octave)
n = 0:127;
x = sin(2 * pi * 0.05 * n);
X = fft(x);
mag = abs(X);
phase = angle(X);
figure;
subplot(3, 1, 1);
plot(n, x, 'k', 'LineWidth', 1.5);
title('Original Signal');
xlabel('Time Index (n)');
ylabel('Amplitude');
grid on;
subplot(3, 1, 2);
plot(mag, 'r', 'LineWidth', 1.5);
title('Magnitude Spectrum');
xlabel('Frequency (FFT Index)');
ylabel('|X(f)|');
grid on;
subplot(3, 1, 3);
plot(phase, 'b', 'LineWidth', 1.5);
title('Phase Spectrum');
xlabel('Frequency (FFT Index)');
ylabel('Phase (radians)');
grid on;
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