I have a noisy set of data that looks roughly like a sine wave. I have taken a Fourier transform of the data, removed noise with a filter, and have taken the inverse Fourier transform of that to make a graph that roughly fits the original data. (All using fftpack in SciPy).
I now want to test how good of a fit this inverse Fourier transform is to the original data using a $\chi^2$ test. My problem is I don't know how to calculate the degrees of freedom to perform this.
Is there any way to find this out?