Cleaning a Brain Signal: What Filtering Changes, and What It Hides

Last post ended with a confirmed 60 Hz spike in the power spectrum — invisible at a wide view, obvious once I zoomed in. This post is the follow-up: what actually happens to the signal once that noise, and everything outside the frequency range I care about, gets filtered out.

The filter

Two things applied together, on the same subject/run from the last post:

Band-pass, 1–40 Hz. Keeps the frequency range where the signals I’m interested in live — motor-imagery work typically looks at the mu (8–13 Hz) and beta (13–30 Hz) bands, so 1–40 Hz keeps that with margin on both sides, while dropping very slow drift below 1 Hz and high-frequency muscle/electronic noise above 40 Hz.
Notch, 60 Hz. Specifically targets the power-line interference confirmed last post, without touching the frequencies right next to it as hard as a wide band-pass cutoff would.

output

Peak power at 60 Hz:
before = 1.395e-11
after  = 1.428e-16
ratio  = 97,686x reduction

A 97,686-times reduction in power at exactly 60 Hz, and nowhere else in the spectrum — that’s what a notch filter is supposed to do: surgical removal of one frequency, not a general cleanup.

What the before/after spectrum shows

Plotted side by side, 0–80 Hz: the “before” spectrum has the expected 1/f-like downward slope plus the 60 Hz spike sitting on top of it. The “after” spectrum keeps the same overall shape through the pass-band, then drops sharply starting around 40 Hz — the band-pass cutoff — down to near-zero power above it, with the 60 Hz spike gone entirely.

The part that’s easy to get wrong

Filter cutoffs are a decision, not a default. 1–40 Hz was not pulled from nowhere — it’s wide enough to keep the mu/beta range I actually need with margin, and narrow enough to drop the worst of the slow drift and high-frequency noise. A different task — say, something that cares about gamma-band activity above 40 Hz — would need a different cutoff entirely, and picking the EEG-textbook default without checking what it keeps or discards for this task is exactly the kind of silent mistake that doesn’t throw an error. Widmann et al., 2015

What I’m taking into the next step

This filter — 1–40 Hz band-pass, 60 Hz notch — becomes the fixed preprocessing step for every experiment after this one, applied identically to every subject, fit before any split happens rather than per-fold (there is nothing data-dependent to leak here; the cutoffs are chosen once, from domain knowledge, not learned from the data). Having the before/after numbers here means that choice is documented, not assumed.

Sources & papers I used while learning this

Widmann et al.2015

Digital filter design for electrophysiological data — a practical approach

Background on why filter choice (cutoffs, filter order, zero-phase vs. causal) is a real methodological decision in EEG processing, not a default to accept blindly.
Read paper