Smoothing of a 1D signal

This method is based on the convolution of a scaled window with the signal. The signal is prepared by introducing reflected window-length copies of the signal at both ends so that boundary effect are minimized in the beginning and end part of the output signal.

Code

import numpy

def smooth(x,window_len=11,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; should be an odd integer
 window: the type of window from 'flat', 'hanning', 'hamming', 'bartlett', 'blackman'
 flat window will produce a moving average smoothing.

 output:
 the smoothed signal

 example:

 t=linspace(-2,2,0.1)
 x=sin(t)+randn(len(t))*0.1
 y=smooth(x)

 see also:

 numpy.hanning, numpy.hamming, numpy.bartlett, numpy.blackman, numpy.convolve
 scipy.signal.lfilter

 TODO: the window parameter could be the window itself if an array instead of a string
 NOTE: length(output) != length(input), to correct this: return y[(window_len/2-1):-(window_len/2)] instead of just y.
 """

    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=numpy.r_[x[window_len-1:0:-1],x,x[-1:-window_len:-1]]
    #print(len(s))
    if window == 'flat': #moving average
        w=numpy.ones(window_len,'d')
    else:
        w=eval('numpy.'+window+'(window_len)')

    y=numpy.convolve(w/w.sum(),s,mode='valid')
    return y

from numpy import *
from pylab import *

def smooth_demo():

    t=linspace(-4,4,100)
    x=sin(t)
    xn=x+randn(len(t))*0.1
    y=smooth(x)

    ws=31

    subplot(211)
    plot(ones(ws))

    windows=['flat', 'hanning', 'hamming', 'bartlett', 'blackman']

    hold(True)
    for w in windows[1:]:
        eval('plot('+w+'(ws) )')

    axis([0,30,0,1.1])

    legend(windows)
    title("The smoothing windows")
    subplot(212)
    plot(x)
    plot(xn)
    for w in windows:
        plot(smooth(xn,10,w))
    l=['original signal', 'signal with noise']
    l.extend(windows)

    legend(l)
    title("Smoothing a noisy signal")
    show()

if __name__=='__main__':
    smooth_demo()

Figure

[](files/attachments/SignalSmooth/smoothsignal.jpg