Python version of Matlab Signal Toolbox's tfestimate()? [closed]

Question

Is there a Python version of Matlab's tfestimate()? I have looked into the control toolbox but it only offers linear transfer functions.

Answer 1

As shown in the 'more about' section of the help of tfestimate, the transfer function is calculated more or less as Txy = Pyx / Pxx, so by dividing the cross-spectral-density between y and x by the power-spectral-density of x. Note that for calculating the cross-spectral density, the order of the arguments is important, since Pyx is calculated (after appropriate windowing and normalization) as the average of fft(y) * conj(fft(x)) over the individual windows. Similarly, the PSD Pxx is calculated as averaging fft(x) * conj(fft(x)). I forgot exactly why, but there is a good reason why you calculate it as the ratio between these two averages, instead of directly averaging fft(y) / fft(x).

Both cpsd and psd are available in matplotlib.mlab, so you can calculate a transfer function more or less like this (untested):

from matplotlib.mlab import psd, csd

def tfe(x, y, *args, **kwargs):
   """estimate transfer function from x to y, see csd for calling convention"""
   return csd(y, x, *args, **kwargs) / psd(x, *args, **kwargs)