import numpy as np
import matplotlib.pyplot as plt

#Frequency array between 0 and 20000 Hz in 1000 steps:
f = np.linspace(0,20000,1000) 

zw = 13*np.arctan(0.00076*f) + 3.5*np.arctan((f/7500)**2)
tr = (26.81*f / (1960 + f)) - 0.53
sr = 7*np.arcsinh(f/650)
wsg = 6*np.arcsinh(f/600)
kov = 8.96*np.log(0.978 + 5*np.log(0.994 + ( (f + 75.4)/2173 )**1.347))

plt.figure(figsize=(10, 7), dpi=300)
plt.plot(f*1e-3,zw, label='Zwicker')
plt.plot(f*1e-3,tr, label='Traunmüller')
plt.plot(f*1e-3,sr, label='Schroeder')
plt.plot(f*1e-3,wsg, label='Wang, Sekey & Gersho')
plt.plot(f*1e-3,kov, label='Kovalchuk')

plt.plot(np.array([100,1270,2700,6400,9500,15500])*1e-3,[1,10,15,20,22,24],\
         'ro', label='Points from the Bark scale')

plt.xlabel('Frequency in kHz')
plt.ylabel('Frequency in Bark')
plt.title('Approximation of the Bark Scale')
plt.legend()
plt.grid()
plt.savefig('Results.png')