Invertibility of Room Impulse Response: Reproducing Research Paper
I wrote the following code for the same purpose and thought of sharing it. For simplicity I assumed impulse response to be simple averaging type(Low Pass Filter).

$h[n]= [0.5,0.5]$

import numpy as np
import matplotlib.pyplot as plt
from scipy import signal

hlp         =   np.array((0.5,0.5))
#hhp        =   np.array((0.5, -0.5))
f, T        =   signal.freqz(hlp)

fig1 = plt.figure()
plt.title('Frequency response')
ax1 = fig1.add_subplot(111)
plt.plot(f, 20 * np.log10(abs(T)), 'b')
plt.ylabel('Amplitude [dB]', color='b')
plt.xlabel('Frequency [rad/sample]')
ax2 = ax1.twinx()
angles = np.unwrap(np.angle(T))
plt.plot(f, angles, 'g')
plt.ylabel('Angle (radians)', color='g')
plt.grid()
plt.axis('tight')

fig2 = plt.figure()
plt.title('Nyquist Plot')
plt.plot(np.real(T), np.imag(T))
plt.ylabel('Im(H(w))')
plt.xlabel('Re(H(w))')
plt.show()


This code resulted the following graphs.


 I plotted this frequency response just for a sanity check(to make sure the numerator and denominator coefficient is taken correctly).



Now I understand it the paper better :-))).