This function is a sum of sines and cosines of the form:
f (x) = a0 + aisinai+1x + ai+2cosai+3x.
You need good initial guess to get this fitting function to
converge quickly, if at all. You will do well to get the
frequencies close. If the zeros of your fitting function
with your initial parameters are close to the zeroes of
your data, you have a good chance of converging. For
special cases like Fourier series, you probably want a
specialized function. You should take a Fourier transform
if that is what you really want.