Try this:
t = linspace(-40, 40, 35);
s1 = sinc(t/10);
s2 = exp(-t.^2/20);
objfcn = @(b,t) b(1).*exp(-b(2)*t.^2) + b(3).*sin(b(4).*t+b(5));
s1prm = fminsearch(@(b) norm(s1 - objfcn(b,t)), rand(5,1)*10)
s2prm = fminsearch(@(b) norm(s2 - objfcn(b,t)), rand(5,1)*10)
figure
plot(t, s1, 'rp', t, s2, 'gp')
hold on
plot(t, objfcn(s1prm,t), '--r')
plot(t, objfcn(s2prm,t), '--g')
hold off
grid
The ‘objfcn’ function is a combination of a sinusoid and a Gaussian. The regression parameters alloow it to fit both kinds of functions reasonablly well.
Experiment to get different (and perhaps better) results. Anoather option of course is to use the fft function to create a Fourier transform of the original waveform, then use a select subset of the Fourier coefficients to reconstruct it.
