Threshold Detection in NumPy

Many signals are easily detected by their size. We will learn how to detect the indices where signals cross a threshold with NumPy. These are our practice signals.

import numpy as np
import matplotlib.pyplot as plt
data = np.array([0, 0, 0, 5, 5, 5, 5, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0])
plt.plot(data, marker='o')

We will perform two simple steps to detect the threshold crossings: 1. Make the data binary, in a way that they are true when larger than the threshold and false when lower or equal. 2. Take the difference of the binary signal. This gives us a boolean array that is true when the threshold was crossed. We can combine those steps into one line.

threshold = 2
threshold_crossings = np.diff(data > threshold, prepend=False)

Plotting shows us that threshold_crossings is true after the threshold was crossed.

plt.plot(data2, marker='o')
plt.plot(thr_crossings, marker='o')
plt.legend(("Data", "Threshold Crossings"))

To get the indices of the threshold crossings we can use np.argwhere(), which returns the true indices from a boolean array.

# array([ 3,  7, 11, 14], dtype=int64)

Threshold crossings occur at 3, 7, 11 and 14. Sometimes we only need the upward or downward crossings. We can simply isolate those by slicing the indiced array.

np.argwhere(threshold_crossings)[::2,0]  # Upward crossings
# array([ 3, 11], dtype=int64)
np.argwhere(thr_crossings)[1::2,0]  # Downward crossings
# array([ 7, 14], dtype=int64)

Sometimes we want to find the point before the threshold is crossed, rather than after. There is one simple trick in np.diff instead of setting prepend=False, we set append=False.

threshold = 2
post_threshold_crossings = np.diff(data > threshold, prepend=False)
pre_threshold_crossings = np.diff(data > threshold, append=False)
plt.plot(data2, marker='o')
plt.plot(post_threshold_crossings, marker ='o')
plt.plot(pre_threshold_crossings, marker='o')
plt.legend(("Data", "Post Crossings", "Pre Crossings"))

Make sure to check out the documentation for np.diff and bonus points if you can figure out why exactly this works. Detecting threshold crossings is an easy but important part in most of my analysis pipelines and now you can do it too.