High-frequency noise is the fast component of signal noise — fluctuations from sample to sample that have no relationship to the underlying signal. Visually, it looks like rapid jitter superimposed on the real curve.
Common sources:
- Electrical interference from nearby equipment in ECG and EEG recordings.
- Mechanical vibration in an Accelerometer picked up from the environment.
- Hiss in audio recordings — thermal noise in the microphone preamp.
- Quantization noise when the sensor’s resolution isn’t quite fine enough for the signal’s amplitude.
The defining property is that the noise varies on a shorter timescale than the real signal. Where Low-frequency noise is a slow drift, high-frequency noise is a fast jitter — and the two are addressed with different tools.
High-frequency noise is removed by smoothing the signal — averaging out the fast fluctuations while preserving the slower features. The simplest smoothing tool is the Moving-average filter, which slides a window along the signal and replaces each sample with the average of its neighborhood. The intuition is the law of large numbers, applied locally: if the noise at each sample is roughly random and equally likely to push up or down, averaging neighboring samples lets the pushes mostly cancel.
The cost of smoothing is feature blurring. A small window barely smooths the signal; only the very fastest fluctuations get averaged out. A large window smooths much more aggressively, but it also blurs genuine fast features and softens sharp transitions. The right window size is the one that suppresses the noise without losing the features of interest — typically chosen empirically.
[Background from general knowledge, not the textbook] Formally, smoothing is a low-pass filter: keep low frequencies (where the real signal lives) and suppress high frequencies (where the noise lives). The moving-average filter is the simplest example. More sophisticated low-pass filters — Butterworth, Chebyshev, FIR designs — give finer control over the frequency response, but the Introduction to Data Science textbook leaves their analytical design for later courses.
For the complementary problem of slowly-varying drift, see Low-frequency noise, which is removed by subtraction rather than smoothing.