Noise is unwanted random variation in a signal — variation that obscures or degrades the information we care about. Real-world signals are always noisy to some degree, because no sensor is perfect, no environment is perfectly quiet, and no transmission channel is lossless.
The distinction worth getting right is noise vs. artifact. Noise hides real features — it adds randomness on top of the signal of interest, making it harder to see what’s there. Artifacts mimic features that don’t exist — they look like signal but aren’t. In the literature the words are often used interchangeably, but in technical conversation precision is worthwhile.
Noise is usually classified by how fast it varies:
- Low-frequency noise is slowly-varying — a gradual drift in the signal’s baseline, like a slow upward slope underneath an otherwise flat measurement. Looks like an offset that itself changes slowly. Examples: thermal drift in a sensor as it warms up, baseline wander in an ECG caused by the patient breathing.
- High-frequency noise is fast-varying — fluctuations from sample to sample that have no relationship to the underlying signal. Looks like rapid jitter superimposed on the real curve. Examples: electrical interference from nearby equipment, mechanical vibration in an accelerometer, hiss in audio.
These two kinds of noise are addressed with different tools:
- Low-frequency noise can often be removed by subtracting a smoothed version of the signal from itself — a high-pass operation.
- High-frequency noise is removed by smoothing the signal — averaging out the fast fluctuations while preserving the slower features. The simplest tool is the Moving-average filter.
The Introduction to Data Science course focuses on high-frequency noise, treating low-frequency noise more briefly. The principle in both cases is the same: separate the noise from the signal by exploiting their different frequency content.
[Background from general knowledge, not the textbook] In signal processing, this separation by frequency is formalized through filters. A low-pass filter keeps low frequencies and removes high ones, suppressing high-frequency noise. A high-pass filter does the reverse, suppressing low-frequency drift. A band-pass filter keeps a specific band of frequencies, which is appropriate for signals like ECG that occupy a known band (roughly 0.5 to 40 Hz). The textbook leaves the analytical design of these filters to later signal-processing courses.