clear all;
close all;
clc;

fs=1000; Ts=1/fs;

f1=20;
DigFreq1=2*pi*f1/fs;
f2=30;
DigFreq2=2*pi*f2/fs;
f3=40;
DigFreq3=2*pi*f3/fs;

N=1500;
n = 0:1:N-1;
t_sample = (0: Ts : (N-1)*Ts);

x=3.*cos(DigFreq1.*n+0.2) + cos(DigFreq2.*n-0.3) + 2.*cos(DigFreq3.*n+2.4);
figure; plot(t_sample, x)

X=fft(x);
X_mag=abs(X);
figure;

Fbin=0:1:N-1;
plot((fs/N).*Fbin, X_mag/(N/2));
xlim([0 fs/2])
set(gca, 'FontSize', 16)
xlabel('$f(Hz)$', 'Interpreter', 'LaTex', 'FontSize', 18);
ylabel('$|X(\omega)|$', 'Interpreter', 'LaTex', 'FontSize', 18);