import numpy as np
import matplotlib.pyplot as plt

N = 1024
t   = np.linspace(0, np.log(N//2 - 1), N)
phi = np.exp(t) - 1
x   = np.cos(2 * np.pi * phi)

#%%######################################
plt.plot(t, x)
plt.show()

plt.plot(t[:-1], np.diff(phi))
plt.axhline(0.5, color='tab:red')
plt.show()