from numpy import sin, cos, pi, linspace
from numpy.random import randn
from scipy.signal import lfilter, lfilter_zi, filtfilt, butter
from matplotlib.pyplot import plot, legend, show, grid, figure, savefig
# Generate a noisy signal to be filtered.
t = linspace(-1, 1, 200)
x = (sin(2 * pi * 0.75 * t*(1-t) + 2.1) + 0.1*sin(2 * pi * 1.25 * t + 1) +
0.18*cos(2 * pi * 3.85 * t))
xn = x + randn(len(t)) * 0.08
# Create an order 3 lowpass butterworth filter.
cut = 1 / (0.5 * 200)
#b, a = butter(3, cut, btype='low')
b, a = butter(3, cut, btype='high')
# Apply the filter to xn. Use lfilter_zi to choose the initial condition
# of the filter.
zi = lfilter_zi(b, a)
z, _ = lfilter(b, a, xn, zi=zi*xn[0])
# Apply the filter again, to have a result filtered at an order
# the same as filtfilt.
z2, _ = lfilter(b, a, z, zi=zi*z[0])
# Use filtfilt to apply the filter.
y = filtfilt(b, a, xn, padlen=1)
# Make the plot.
figure(figsize=(10,5))
plot(t, xn, 'b', linewidth=1.75, alpha=0.75)
#plot(t, z, 'r--', linewidth=1.75)
#plot(t, z2, 'r', linewidth=1.75)
plot(t, y, 'k', linewidth=1.75)
legend(('noisy signal',
'filtfilt'),
loc='best')
grid(True)
show()
#savefig('plot.png', dpi=65)
