How to remove a drifting baseline from a sensor signal

To remove a slow drift from a sensor signal and keep the quick changes, subtract a low-pass from the reading: fast = reading - slow, where slow is an exponential filter following the reading. Whatever the low-pass keeps, the subtraction throws away, so the result is a high-pass filter with the same cutoff. Put the cutoff between the drift and the signal you want.

Subtract the slow part

slow = slow + (reading - slow) * 0.05;
fast = reading - slow;

slow follows the drifting baseline, and fast is whatever rides on top of it. If the reading is 640 and slow is 600, fast is 40. Add the two parts back together and you get the reading exactly, slow + (reading − slow) = reading, so nothing is lost: the signal is just split into a slow part and a fast part.

A lighthouse at dawn

A light sensor watches a lighthouse flash once a second, each flash about 100 counts brighter than the gaps, while dawn lifts the whole sky from about 200 to over 700 in 8 seconds. A fixed line at 230 catches the first flash, then the brightening sky climbs past it and every moment looks like a flash: it sees 1 of 8. A line at fast > 40 rides along on the sky and sees all 8.

Choose the cutoff

A fingertip pulse sensor sees each heartbeat, about 1.2 Hz, riding on breathing at about 0.2 Hz. A cutoff between them, about 0.6 Hz, removes the breathing and keeps the beats: alpha 0.04 at 100 samples a second. Set it far too low, alpha 0.002 for about 0.03 Hz, and the breathing passes straight through with the beats, pushing some of them under the line.

The lag leaves an offset

slow follows the drift a little late, so while the baseline is rising, fast sits slightly above zero. That's why the line goes at 40 rather than just above 0. A higher cutoff tracks a fast drift more closely, at the cost of shrinking the slower parts of the signal you wanted to keep.

Where you'll meet it

Heart-rate monitors and pulse oximeters remove breathing and finger movement this way. ECG machines filter out baseline wander with a cutoff typically between 0.05 and 0.5 Hz. An oscilloscope's AC coupling does the same job with a capacitor, and a burglar alarm's motion sensor reacts to changes in heat, not to a warm room.