Wigner-Hough Transform of a Chirp

This example demonstrates the use of the Hough transform to extract the estimates of a chirp signal from its Wigner Ville distribution.

Figure 5.4 from the tutorial.

/home/docs/checkouts/readthedocs.org/user_builds/tftb/checkouts/stable/doc/_gallery/plot_5_4_2_hough_noisy_chirp.py:34: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
  ax = fig.gca(projection='3d')

import numpy as np
from tftb.generators import noisecg, sigmerge, fmlin
from tftb.processing.cohen import WignerVilleDistribution
from tftb.processing.postprocessing import hough_transform
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

N = 64
sig = sigmerge(fmlin(N, 0, 0.3)[0], noisecg(N), 1)
tfr, _, _ = WignerVilleDistribution(sig).run()

ht, rho, theta = hough_transform(tfr, N, N)
theta, rho = np.meshgrid(theta, rho)
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_wireframe(theta, rho, ht)
ax.set_xlabel('Theta')
ax.set_ylabel('Rho')
plt.show()