Warning: This post is several years old and the author has marked it as poor quality (compared to more recent posts). It has been left intact for historical reasons, but but its content (and code) may be inaccurate or poorly written.

I wrote discrete functions to perform data smoothing in python. I found this Gaussian smoothing function to be most useful:

def smoothListGaussian(list, degree=5):
    window = degree*2-1
    weight = numpy.array([1.0]*window)
    weightGauss = []
    for i in range(window):
        i = i-degree+1
        frac = i/float(window)
        gauss = 1/(numpy.exp((4*(frac))**2))
        weightGauss.append(gauss)
    weight = numpy.array(weightGauss)*weight
    smoothed = [0.0]*(len(list)-window)
    for i in range(len(smoothed)):
        smoothed[i] = sum(numpy.array(list[i:i+window])*weight)/sum(weight)
    return smoothed 

Provide a list and it will return a smoother version of the data. The Gaussian smoothing function I wrote is leagues better than a moving window average method, for reasons that are obvious when viewing the chart below. Surprisingly, the moving triangle method appears to be very similar to the Gaussian function at low degrees of spread. However, for huge numbers of data points, the Gaussian function should perform better.

import pylab
import numpy

def smoothList(list, strippedXs=False, degree=10):
    if strippedXs == True:
        return Xs[0:-(len(list)-(len(list)-degree+1))]
    smoothed = [0]*(len(list)-degree+1)
    for i in range(len(smoothed)):
        smoothed[i] = sum(list[i:i+degree])/float(degree)
    return smoothed

def smoothListTriangle(list, strippedXs=False, degree=5):
    weight = []
    window = degree*2-1
    smoothed = [0.0]*(len(list)-window)
    for x in range(1, 2*degree):
        weight.append(degree-abs(degree-x))
    w = numpy.array(weight)
    for i in range(len(smoothed)):
        smoothed[i] = sum(numpy.array(list[i:i+window])*w)/float(sum(w))
    return smoothed

def smoothListGaussian(list, strippedXs=False, degree=5):
    window = degree*2-1
    weight = numpy.array([1.0]*window)
    weightGauss = []
    for i in range(window):
        i = i-degree+1
        frac = i/float(window)
        gauss = 1/(numpy.exp((4*(frac))**2))
        weightGauss.append(gauss)
    weight = numpy.array(weightGauss)*weight
    smoothed = [0.0]*(len(list)-window)
    for i in range(len(smoothed)):
        smoothed[i] = sum(numpy.array(list[i:i+window])*weight)/sum(weight)
    return smoothed

### DUMMY DATA ###
data = [0]*30  # 30 "0"s in a row
data[15] = 1  # the middle one is "1"

### PLOT DIFFERENT SMOOTHING FUNCTIONS ###
pylab.figure(figsize=(550/80, 700/80))
pylab.suptitle('1D Data Smoothing', fontsize=16)
pylab.subplot(4, 1, 1)
p1 = pylab.plot(data, ".k")
p1 = pylab.plot(data, "-k")
a = pylab.axis()
pylab.axis([a[0], a[1], -.1, 1.1])
pylab.text(2, .8, "raw data", fontsize=14)
pylab.subplot(4, 1, 2)
p1 = pylab.plot(smoothList(data), ".k")
p1 = pylab.plot(smoothList(data), "-k")
a = pylab.axis()
pylab.axis([a[0], a[1], -.1, .4])
pylab.text(2, .3, "moving window average", fontsize=14)
pylab.subplot(4, 1, 3)
p1 = pylab.plot(smoothListTriangle(data), ".k")
p1 = pylab.plot(smoothListTriangle(data), "-k")
pylab.axis([a[0], a[1], -.1, .4])
pylab.text(2, .3, "moving triangle", fontsize=14)
pylab.subplot(4, 1, 4)
p1 = pylab.plot(smoothListGaussian(data), ".k")
p1 = pylab.plot(smoothListGaussian(data), "-k")
pylab.axis([a[0], a[1], -.1, .4])
pylab.text(2, .3, "moving gaussian", fontsize=14)
# pylab.show()
pylab.savefig("smooth.png", dpi=80)

This data needs smoothing. Below is a visual representation of the differences in the methods of smoothing.

The degree of window coverage for the moving window average, moving triangle, and Gaussian functions are 10, 5, and 5 respectively. Also note that (due to the handling of the “degree” variable between the different functions) the actual number of data points assessed in these three functions are 10, 9, and 9 respectively. The degree for the last two functions represents “spread” from each point, whereas the first one represents the total number of points to be averaged for the moving average.