import pyfar as pf
import numpy as np
import matplotlib.pyplot as plt
x = pf.signals.impulse(2**17)
y = pf.dsp.filter.fractional_octave_bands(
    x, 1, frequency_range=(20, 8e3))
y_sum = pf.FrequencyData(
    np.sum(np.abs(y.freq)**2, 0), y.frequencies)
pf.plot.freq(y)
ax = pf.plot.freq(y_sum, color='k', log_prefix=10, linestyle='--')
ax.set_title(
    "Filter bands and the sum of their squared magnitudes")