Step change detection in signal by convolving with step vector

Question

I am facing the following problem in signal processing and I have run into a wall. I am trying to detect abrupt changes (step changes) in a constantly decreasing signal by convolving the signal with a step vector as described here. Well, for some data it works pretty well and I get what I want, but for other data the global minimum for convolution is not exactly in the sharpest step decrease.

I have the following signal:

Please consider the following code in python:

data = 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data -= np.average(data)
steps = np.hstack((np.ones(len(data)), -1*np.ones(len(data))))
convolution = np.convolve(data, steps, mode='valid')
globalMinIndex = np.argmin(convolution)

plt.figure()
plt.plot(data)
plt.plot(convolution/10)

The (incorrect) result:

As you can see, the global minimum is reached at a place, where the signal after standarization revolves around zero. But I would rather expect it to be at the sharpest step in the signal.

Please consider, the following data, where this algorithm works exactly as expected:

The (correct) result:

My questions are:

1. Do you know the name of this method for step detection? I have been searching but couldn't find anything specific/formal regarding this method.

2. Why does it fail for the first data set? Is there a better way to standardize this data or use a different convolution filter so that it yields the correct result consistently?

I have been trying to find the reason why it fails but have run out of ideas. Thank you.

Answer 1

You are right, this method certainly does not work in your case. I hope to edit my answer to provide an explanation for why that is. For now, I'll demonstrate that you can achieve the result you want by simply using a shorter filter.

filter_len = 15

data = 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data -= np.average(data)
steps = np.hstack([np.ones(filter_len), -1*np.ones(filter_len)])
convolution = np.convolve(data, steps, mode='valid')
globalMinIndex = np.argmin(convolution)+filter_len-1
plt.figure()
ax = plt.gca()
ax.plot(data)
ax2 = ax.twinx()
plt.grid(b=False)
ax2.plot(range(filter_len-1, len(data)-filter_len),convolution/10, c="orange", alpha=0.5)