Over a million developers have joined DZone.

Computing Convolution using Numpy's Kaiser Windows

DZone's Guide to

Computing Convolution using Numpy's Kaiser Windows

· Web Dev Zone
Free Resource

Start coding today to experience the powerful engine that drives data application’s development, brought to you in partnership with Qlik.

A convolution is a way to combine two sequences, x and w, to get a third sequence, y, that is a filtered version of x. The convolution of the sample x t is computed as follows:

It is the mean of the weighted summation over a window of length k and w t are the weights. Usually, the sequence w is generated using a window function. Numpy has a number of window functions already implemented: bartlett, blackman, hamming, hanning and kaiser. So, let's plot some Kaiser windows varying the parameter beta:

import numpy
import pylab

beta = [2,4,16,32]

for b in beta:
 w = numpy.kaiser(101,b) 
 pylab.plot(range(len(w)),w,label="beta = "+str(b))

The graph would appear as follows:

And now, we can use the function convolve(...) to compute the convolution between a vector x and one of the Kaiser window we have seen above:

def smooth(x,beta):
 """ kaiser window smoothing """
 # extending the data at beginning and at the end
 # to apply the window at the borders
 s = numpy.r_[x[window_len-1:0:-1],x,x[-1:-window_len:-1]]
 w = numpy.kaiser(window_len,beta)
 y = numpy.convolve(w/w.sum(),s,mode='valid')
 return y[5:len(y)-5]

Let's test it on a random sequence:

# random data generation
y = numpy.random.random(100)*100 
for i in range(100):
 y[i]=y[i]+i**((150-i)/80.0) # modifies the trend

# smoothing the data
pylab.plot(y,'-k',label="original signal",alpha=.3)
for b in beta:
 yy = smooth(y,b) 
 pylab.plot(yy,label="filtered (beta = "+str(b)+")")

The program would have an output similar to the following:

As we can see, the original sequence have been smoothed by the windows.

Source: http://glowingpython.blogspot.com/2012/02/convolution-with-numpy.html

Create data driven applications in Qlik’s free and easy to use coding environment, brought to you in partnership with Qlik.


Opinions expressed by DZone contributors are their own.


Dev Resources & Solutions Straight to Your Inbox

Thanks for subscribing!

Awesome! Check your inbox to verify your email so you can start receiving the latest in tech news and resources.


{{ parent.title || parent.header.title}}

{{ parent.tldr }}

{{ parent.urlSource.name }}