How can I add sinusoidal signal and fft?

I have to add 4 sinusoidal signal and plot the spectrum. How can ı do it I dont know. After adding the signals İ will use fft. Please help me ı can not find sources. I will generate sinusoidal signals.

Answer 1

[Chunru]

fs = 1000;
f = [40 80 100 250];        % freq
a = [1 2 3 1];              % amp
p = randn(1,4)*2*pi;        % phase

t = (0:1/fs:1.023)';
x = a.*cos(2*pi*f.*t + p);
figure; plot(t, x);

L=1024;
xtotal = sum(x, 2);
y = fft(xtotal, L);
P2 = abs(y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);

figure
faxis = fs*(0:(L/2))/L;
plot(faxis, 20*log10(P1)) 

[studentmatlaber]

Thank you so much. Can i ask a question? Do these 4 signals have different spikes of the spectrum because they have different amplitude and frequency values?

[Chunru]

You are right.