"""
cookb_signalsmooth.py
from: http://scipy.org/Cookbook/SignalSmooth
"""
import numpy as np
import matplotlib.pyplot as plt
[docs]
def smooth(x, window_len=10, window='hanning'):
"""smooth the data using a window with requested size.
This method is based on the convolution of a scaled window with the signal.
The signal is prepared by introducing reflected copies of the signal
(with the window size) in both ends so that transient parts are minimized
in the begining and end part of the output signal.
input:
x: the input signal
window_len: the dimension of the smoothing window
window: the type of window from 'flat', 'hanning', 'hamming', 'bartlett', 'blackman'
flat window will produce a moving average smoothing.
output:
the smoothed signal
example:
import numpy as np
t = np.linspace(-2,2,0.1)
x = np.sin(t)+np.random.randn(len(t))*0.1
y = smooth(x)
see also:
numpy.hanning, numpy.hamming, numpy.bartlett, numpy.blackman, numpy.convolve
scipy.signal.lfilter
NOTE from B. Chen: slightly modified the reflected copies: window_len-1 points are added to both ends.
Previous one is not exactly the reflection, the indices are off by one pixel
"""
if x.ndim != 1:
raise(ValueError, "smooth only accepts 1 dimension arrays.")
if x.size < window_len:
raise(ValueError, "Input vector needs to be bigger than window size.")
if window_len < 3:
return x
if not window in ['flat', 'hanning', 'hamming', 'bartlett', 'blackman']:
raise(ValueError, "Window is on of 'flat', 'hanning', 'hamming', 'bartlett', 'blackman'")
#s=np.r_[2*x[0]-x[window_len:1:-1], x, 2*x[-1]-x[-1:-window_len:-1]]
s=np.r_[2*x[0]-x[window_len-1:0:-1], x, 2*x[-1]-x[-2:-window_len-1:-1]]
#print(len(s))
if window == 'flat': #moving average
w = np.ones(window_len,'d')
else:
w = getattr(np, window)(window_len)
y = np.convolve(w/w.sum(), s, mode='same')
return y[window_len-1:-window_len+1]
#*********** part2: 2d
from scipy import signal
[docs]
def gauss_kern(size, sizey=None):
""" Returns a normalized 2D gauss kernel array for convolutions """
size = int(size)
if not sizey:
sizey = size
else:
sizey = int(sizey)
x, y = np.mgrid[-size:size+1, -sizey:sizey+1]
g = np.exp(-(x**2/float(size) + y**2/float(sizey)))
return g / g.sum()
[docs]
def blur_image(im, n, ny=None) :
""" blurs the image by convolving with a gaussian kernel of typical
size n. The optional keyword argument ny allows for a different
size in the y direction.
"""
g = gauss_kern(n, sizey=ny)
improc = signal.convolve(im, g, mode='valid')
return(improc)
[docs]
def smooth_demo():
t = np.linspace(-4,4,100)
x = np.sin(t)
xn = x + np.random.randn(len(t)) * 0.1
y = smooth(x)
ws = 31
plt.subplot(211)
plt.plot(np.ones(ws))
windows=['flat', 'hanning', 'hamming', 'bartlett', 'blackman']
plt.hold(True)
for w in windows[1:]:
#eval('plt.plot('+w+'(ws) )')
plt.plot(getattr(np, w)(ws))
plt.axis([0,30,0,1.1])
plt.legend(windows)
plt.title("The smoothing windows")
plt.subplot(212)
plt.plot(x)
plt.plot(xn)
for w in windows:
plt.plot(smooth(xn,10,w))
l = ['original signal', 'signal with noise']
l.extend(windows)
plt.legend(l)
plt.title("Smoothing a noisy signal")
#plt.show()
if __name__=='__main__':
# part 1: 1d
smooth_demo()
# part 2: 2d
X, Y = np.mgrid[-70:70, -70:70]
[docs]
Z = np.cos((X**2+Y**2)/200.)+ np.random.normal(size=X.shape)
Z2 = blur_image(Z, 3)
plt.figure()
plt.imshow(Z)
plt.figure()
plt.imshow(Z2)
plt.show()