% generating signal x1
Fs = 100;        % sampling frequency
t = [0 : 1/Fs : 10];
x1 = 4 * cos(2 * pi * 3.5 * t - ((30*pi)/180));

% 1000 and 4000 point fft of signal x1
X1000 = fft(x1, 1000);
X1000_mag = abs(X1000);     % magnitude spectrum
X1000_mag = fftshift(X1000_mag);
X1000_phase = angle(X1000);     % phase spectrum
X1000_phase = fftshift(X1000_phase);

X4000 = fft(x1, 4000);
X4000_mag = abs(X4000);     % magnitude spectrum
X4000_mag = fftshift(X4000_mag);
X4000_phase = angle(X4000);     % phase spectrum
X4000_phase = fftshift(X4000_phase);

% plots the 1000 and 4000 point magnitude and phase spectrums
N1000 = length(X1000);
N4000 = length(X4000);
F1000 = Fs * [-N1000/2: N1000/2 - 1]/N1000;
F4000 = Fs * [-N4000/2: N4000/2 - 1]/N4000;
figure; hold on;
plot(F1000, X1000_mag);
plot(F4000, X4000_mag);
xlabel('Frequency (Hz)');
ylabel('Magnitude (A.U.)');
title('Magnitude Spectrum of Signal x1');

figure; hold on;
plot(F1000, X1000_phase);
plot(F4000, X4000_phase);
xlabel('Frequency (Hz)');
ylabel('Phase (rads)');
title('Phase Spectrum of Signal x1');

% generating signal x2 and x_tot
x2 = 3 * cos(2 * pi * 3.62 * t);
x_tot = x1 + x2;

% 1000 and 4000 point fft of signal x_tot
X1000_tot = fft(x_tot, 1000);
X1000_tot_mag = abs(X1000_tot);     % magnitude spectrum
X1000_tot_mag = fftshift(X1000_tot_mag);
X1000_tot_phase = angle(X1000_tot);     % phase spectrum
X1000_tot_phase = fftshift(X1000_tot_phase);

X4000_tot = fft(x_tot, 4000);
X4000_tot_mag = abs(X4000_tot);     % magnitude spectrum
X4000_tot_mag = fftshift(X4000_tot_mag);
X4000_tot_phase = angle(X4000_tot);     % phase spectrum
X4000_tot_phase = fftshift(X4000_tot_phase);

% plots the 1000 and 4000 point magnitude and phase spectrums
figure; hold on;
plot(F1000, X1000_tot_mag);
plot(F4000, X4000_tot_mag);
xlabel('Frequency (Hz)');
ylabel('Magnitude (A.U.)');
title('Magnitude Spectrum of Signal xtot');

figure; hold on;
plot(F1000, X1000_tot_phase);
plot(F4000, X4000_tot_phase);
xlabel('Frequency (Hz)');
ylabel('Phase (rads)');
title('Phase Spectrum of Signal xtot');