Basically suppose on was given an unknown function/data and expected to write a function so that $Y=f(X)$, this can be done by linear regression in simple cases very easily. However, suppose that the out put $Y$ was an extreme chaotic curves, then the curve fitting become problematic, and the regression, in practice, largely dependent on the people's feeling/choice. Although there's several complete basis so that the expansion can be reduced much less, there's still question about weather one be able to fit the data after considering large sets of equations/combinations of functions.
I recently thought of the cases in calculus where we use polynomial to reexamine the original function. In corresponding, on can obtain sets of lists of function in Fourier domain, where the functions were represented by sets of coefficients. Thus, instead of fitting the data by comparing non arbitrary or even problematic fitting, one might be able to simply fit the function in Fourier domain in terms of very simple linear coefficient fitting.
My questions were:
Is that possible?
Are there other methods to fit the non chaotic function in large sample and combinations?