How do I deconstruct a signal with fast fourier transformation in Python?
If you have a periodic signal, that is a repeating waveform, you can most easily find the constituent component parameters by aligning the Discrete Fourier Transform (DFT) frame on a whole number of cycles.  Suppose you chose four.  Then bins 0, 4, 8, 12, etc. contain the relevant values.

For a signal:

$$ x[n] = A \cos( \omega n + \phi ) $$

If

$$ \omega = \frac{2\pi}{N} k $$

where $k$ (cycles per frame) is an integer, then the $k$th bin will have a value of

$$ X[k] = \frac{A}{2} e^{i\phi} $$

So, you can read the tone's parameters right from the magnitude and angle of the DFT bin.  (FFT is an implementation of DFT)

If you aren't aligned on a whole number of bins, there is an interative process you can do with the formulas found in my blog articles.  This takes considerably more calculations though.