function fid
hold off
% Define the time domain
nmax=10; n=2^nmax; tmax=20; dt=tmax/(n-1); t=[0:dt:tmax];
% Specify frequencies and amplitudes
omega=[15 25 35 45]; amp=[1 2 3 4]; nt=length(t); nfreq=length(omega);
tau=5;
for i=1:nt
    time=t(i); s=0;
    for j=1:nfreq
    s=s+amp(j)*cos(omega(j)*time)*exp(-time/tau); end
    f(i)=s;
end
y=real(fft(f));
w=2*pi*[1:length(y)]/20;
% Plot the original signal - "free induction decay"
subplot(2,1,1)
plot(t,f,'-k','linewidth',1)
ylabel('$f(t)$','Interpreter','latex','fontsize',30)
xlabel('$t$','Interpreter','latex','fontsize',30)
axis([0 10 -8 8])
set(gca,'FontSize',26)
set(gca,'Ytick',[-8:8:8],'linewidth',1.6)
set(gca,'Xtick',[0:5:10],'linewidth',1.6)
% Calculate the FFT
y=real(fft(f));
% Plot the Fourier transform giving the original frequencies
subplot(2,1,2)
plot(w,y,'-k','linewidth',1.2)
ylabel('$f(\omega)$','Interpreter','latex','fontsize',30)
xlabel('$\omega$','Interpreter','latex','fontsize',30)
axis([0 60 0 400])
set(gca,'FontSize',26)
set(gca,'Ytick',[0:200:400],'linewidth',1.6)
set(gca,'Xtick',[5:10:60],'linewidth',1.6)
axis([1 60 0 400])