Taking the area under a square pulse

Question

Hey Stack Overflow community,

I've been given a series of datasets that resembles a square pulse, and ideally looks like the following:

This particular plot is composed of many sets of data.

I'm wondering if there is a way to reduce the noise found in the data, and retrieve just the area under the square pulse with the assumption that "spikes" may appear before or on the actual pulse itself.

The method I've tried is to cut everything before and after the pulse, and look for spikes that may occur on the actual pulse by looking at how much each value deviates from the mode peak found. However, this seems less than adequate as my implementation requires going through each point multiple times generating quite a large time complexity, and the file sizes are pretty huge.

Thanks for helping out!

Answer 1

A good strategy in the presence of white noise would be to do a moving average over the number of samples that equals the length of the pulse. The peak of this moving average will be your area with the noise optimally minimized.

So if you use MATLAB or Octave it would be as simple as this, assuming the pulse is 200 samples wide:

out = filter(ones(200,1),1,in);
area = max(out);

Or otherwise convolve your data with a sequence of 200 ones.

Using the Python scipy.signal package this is equivalently:

out = sig.lfilter(np.ones(200,1),1,in) 
area = np.max(out)