Use nls().
But you should also take the time to learn a bit about data fits in
general. I'm far from expert, but it sure looks like that P(t) is
overconstrained. Since cos(wt) = sin(wt+pi/2), why do you have all
those different terms?
<quote>
Dear all,
I have a time series and I like to fit S(t) = T(t) + P(t)
T(t) = Linear Trend = a + bt
P(t) = Periodic Signal = sum(Ai*cos(wt) + Bi*sin(wt) ) for i=1,...,3.
</quote>
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