You have a time series of N points. You could use normal curve fitting to fit a constant function + (N-1) sine and cosine waves, and it turns out there is alway

You have a time series of N points. You could use normal curve fitting to fit a constant function + (N-1) sine and cosine waves, and it turns out there is always a perfect fit, whatever your N points are. Discrete fourier transform is "just" a faster way to compute the same result.