# Implement a matched filter using cross-correlation, to recover a signal
# that has passed through a noisy channel.

from scipy import signal
sig = np.repeat([0., 1., 1., 0., 1., 0., 0., 1.], 128)
sig_noise = sig + np.random.randn(len(sig))
corr = signal.correlate(sig_noise, np.ones(128), mode='same') / 128

import matplotlib.pyplot as plt
clock = np.arange(64, len(sig), 128)
fig, (ax_orig, ax_noise, ax_corr) = plt.subplots(3, 1, sharex=True)
ax_orig.plot(sig)
ax_orig.plot(clock, sig[clock], 'ro')
ax_orig.set_title('Original signal')
ax_noise.plot(sig_noise)
ax_noise.set_title('Signal with noise')
ax_corr.plot(corr)
ax_corr.plot(clock, corr[clock], 'ro')
ax_corr.axhline(0.5, ls=':')
ax_corr.set_title('Cross-correlated with rectangular pulse')
ax_orig.margins(0, 0.1)
fig.tight_layout()
fig.show()