Say I have two signals, a(t) and b(t) where the former is the input and the latter in the output. These signals are both recorded by sampling at every 0.01s. The Fast Fourier Transform was applied to both of these providing me with two large arrays of complex numbers. The FFT of b was divided by the FFT of a to provide me with a new array of complex numbers. This was plotted as can be seen below:
Where x axis is real any y axis is imaginary.
How would one go about producing a closed form type polynomial for the transfer function of such a system?
Edit: Inverse FFT of the above. Complex components were of the order e^-14 and thus rounded to 0.