Low-frequency noise is the slow component of signal noise — a gradual drift in the signal’s baseline, varying on a much longer timescale than the features we’re interested in. Visually, it looks like an offset that itself changes slowly, sliding the signal up or down across the recording.
Common sources:
- Thermal drift in a sensor as it warms up. The output reading changes slowly even though the physical quantity being measured isn’t.
- Baseline wander in an ECG caused by the patient breathing, the chest rising and falling under the electrodes.
- Electrode polarization changing over the course of a long recording.
- DC offset shifts in the analog electronics, particularly in cheap consumer-grade sensors.
The defining property is that the noise varies on a longer timescale than the real signal. An ECG heartbeat lasts roughly a second; baseline wander from breathing varies on a four-second timescale. They’re separable in frequency.
The standard response is a high-pass operation — subtract a smoothed version of the signal from itself. The smoothed version captures the slow drift; subtracting it removes the drift while leaving the fast features intact. [Background from general knowledge, not the textbook] Formally, this is a high-pass filter, which can be designed analytically using signal-processing tools (Butterworth, Chebyshev, FIR filters with specified cutoffs). The Introduction to Data Science textbook leaves the analytical design for later courses.
For the complementary problem — fast-varying noise that adds jitter to each sample — see High-frequency noise, which is removed by smoothing rather than subtraction. The two kinds of noise need different tools; mixing them up wastes effort.