clear all; close all;
f = (1:4)';  %Some frequencies
w = 2*pi*f;
ph = (0:.25:.75)';  
tmax = 1;
dt = 1/1024;
t = 0:dt:tmax-dt;
tl = length(t);
ph = repmat(ph, 1, tl);
vi = sin(w*t+ph);  %The individual sinusoids
figure
plot (t, vi);
v = sum(vi);  
figure
plot(t,v)  %plot of the reference signal
grid on
si=1:tl/16:tl; 
vs = zeros(1, tl);
vs(si) = v(si);  
figure
stem(t, vs)
Vs = (tl/16)*fft(vs);  
f = 0:1/tmax: 1/dt-tmax;
figure
plot(f, 20*log10(abs(Vs)));
ufi = 4;  
Vsf = Vs;
Vsf(ufi+2:end-ufi) = eps;  
figure
plot(f, 20*log10(abs(Vsf)));
vsf = ifft(Vsf);  
figure
plot(t, vsf)  %This should match the reference signal
grid on