Is it really an oscillation?

Why this matters

“Alpha power increased” sounds like a claim about a rhythm and is not one. Band power is the area under the spectrum in a frequency range, and the spectrum in that range is mostly the aperiodic background; a band-power change can happen with no peak in the band, no rhythm in the data, and nothing to desynchronize. Even where a peak exists, the rhythm behind it is usually not continuous: threshold its envelope and “sustained alpha” resolves into a handful of bursts — and the number of bursts you find moves by a factor of eleven on the threshold alone, with the signal untouched. This lesson is the set of checks that has to happen before a band-power number is reported as a rhythm.

Concepts

Band power is not a rhythm

L1.7 separated a spectrum into an aperiodic component — broadband, falling with frequency, parameterised by an offset and an exponent — and whatever periodic peaks sit on top of it. Band power integrates the whole thing. So three different events all read as “more beta”:

• a genuine increase in a beta rhythm sitting on an unchanged background;
• an unchanged rhythm on a background whose offset rose, which raises every band together;
• a background whose exponent changed, which raises power at one end of the spectrum and lowers it at the other, with a pivot somewhere in between.

Only the first is a statement about an oscillation, and band power cannot tell them apart. The diagnostic is pf-band-power-slope, and its figure makes the case on real data: in a band chosen by rule to have no fitted peak in either condition, band power still changes by a median factor of 1.19 between eyes open and eyes closed, and the aperiodic fit alone predicts a factor of 1.17 — 96 % of the change, in a band with no rhythm in it.

The check is cheap. Fit the spectrum, look for a peak in the band, and report the aperiodic parameters alongside any band-power claim. (Donoghue, 2022) sets out the argument and the failure modes; the practical rule is that a band-power result without a peak in the band is a result about the aperiodic component and should be reported as one. If a peak is present, report its centre frequency, power and bandwidth, and prefer the peak’s own parameters to band power wherever the question allows.

Individualized bands

Canonical band edges are conventions — and mismatched conventions, at that: one lab’s alpha is 8–12 Hz, another’s 8–13, another’s 7.5–12.5. When a peak exists, the individual’s own peak frequency is a better anchor than any of them, because an 8–12 Hz band measures a different part of the spectrum in a person whose peak is at 9 Hz than in one whose peak is at 11.5 Hz, and age, arousal and task all move it.

The usual construction is the fitted peak centre plus or minus a fixed width — the shipped asset’s own individual_alpha block records a peak at 10.272 Hz and a band of 8.27–12.27 Hz, which is the peak ± 2 Hz. Note what that is: the peak is a measurement and the ± 2 Hz is a convention, and the sidecar says so. A defensible alternative is to take the band edges from the fitted peak’s own bandwidth rather than from a fixed number. Either way, individualising the band means the band differs between subjects, which has to be stated — and a subject with no fitted peak has no band to individualise, which is the previous section’s problem arriving again.

Bursts

A spectral peak says there is a rhythm somewhere in the record. It does not say the rhythm was running continuously, and for most cortical rhythms it was not: (Jones, 2016) argues the case for transient events as the basic unit. The consequence for analysis is direct. If a rhythm is present 20 % of the time at high amplitude, then average band power confounds how often it occurred with how large it was, and two recordings with the same mean power can differ completely in both.

Detecting bursts from an amplitude envelope is simple to describe and full of free parameters:

1. Band-pass to the band of interest, ideally the individual’s own.
2. Envelope — the magnitude of the analytic signal (L4.3).
3. Threshold — a percentile of the envelope, a multiple of its median, or an absolute value.
4. Minimum duration — usually stated in cycles of the band centre, to reject single noise excursions.
5. Statistics — count, rate, mean duration, duty cycle, mean amplitude.

Steps 3 and 4 are decisions with no agreed answer, and the results move a very long way across the range a reasonable person would accept. On the 60-second eyes-closed segment the widget serves, with the alpha band, a 3-cycle minimum and the filter’s contaminated edges excluded:

The burst rate falls by a factor of eleven and the duty cycle by a factor of sixteen, on the threshold alone. Nothing about the recording changed between those rows. That is not an argument against burst analysis; it is the reason a burst result has to travel with its threshold rule, its minimum duration, its band, and a sensitivity analysis showing what happens across the range of each.

Two smaller decisions matter more than they look. The minimum duration rounding rule can move a count on its own: on this asset, requiring a run to cover three cycles of the 10.5 Hz band centre needs 72 samples at 250 Hz, where the data script’s stated 0.284 s minimum is 71 — and at the 75th-percentile threshold that single sample is the difference between 19 bursts and 20. And the edges: a zero-phase FIR of N taps contaminates (N−1)/2 samples at each end, 0.82 s here for the 413-tap alpha filter, so bursts inside that strip are artefacts of the filter and the statistics exclude them by default (pf-tf-edge-effects).

Cycle-by-cycle, and non-sinusoidal waveforms

The envelope approach still assumes the rhythm is a sine wave whose amplitude is modulated. Cycle-by-cycle analysis drops that assumption: identify individual cycles from the raw trace by their peaks and troughs, and measure each one — period, amplitude, rise-decay asymmetry (is the rising flank faster than the falling one?) and peak-trough asymmetry (is the peak sharper than the trough?) — then call a run of consecutive cycles a burst when the features are consistent enough. (Cole, 2017) and (Cole et al., 2019) develop the method and the argument behind it.

The argument is that waveform shape is signal, not nuisance, and that the spectrum disguises it. A perfectly periodic but non-sinusoidal rhythm — a sawtooth, an arch, anything with a sharp trough — must have energy at integer multiples of its fundamental, because that is what a Fourier series of a non-sinusoidal periodic function is. Three consequences follow, and all three appear elsewhere in this level:

• a fitted “beta peak” at exactly twice a subject’s alpha peak may be alpha’s harmonic rather than a beta rhythm;
• phase-amplitude coupling between a rhythm and its own harmonic is produced by the waveform alone, with no second oscillator (pf-harmonics-as-pac, L4.5);
• a change in waveform shape with no change in amplitude changes band power at the harmonic, which reads as a change in a different “rhythm”.

The check is to look at the waveform. A cycle-averaged trace, or simply a few seconds of the raw signal beside its band-passed version, settles most cases in a glance.

Two ways the filter answers the question for you

A narrow filter makes anything rhythmic. Band-pass white noise to 2 Hz and the output rises and falls smoothly at the band centre, because that is what the filter passes. pf-narrowband-filter-oscillation shows it on a real recording that has no spectral peak in the band tested: the filtered trace looks rhythmic, and a phase-randomised surrogate with the same power spectrum and no waveform structure looks exactly as rhythmic. A band-passed trace is evidence about the filter; the evidence for an oscillation is a peak above the aperiodic fit.

A hardware filter can remove the peak you are looking for. An amplifier with a notch at the mains frequency, or a low-pass roll-off at 40–50 Hz, leaves a hole or a slope in the spectrum that has nothing to do with the brain — and a second, software notch on top of the first widens it. That is pf-notch-hole-in-band, and it is a reason to read the recording’s own hardware settings before fitting anything: the fit will happily model an instrument’s response as an aperiodic component or as the absence of a peak.

The data behind this lesson

• The burst widget: ds-lemon, sub-010002, channel O2, 60 s of eyes-closed rest starting at t = 378.03 s, resampled 2500 → 250 Hz with an anti-alias low-pass, DC offset removed, and otherwise unfiltered — the widget runs filter-Hilbert itself, so the band and the threshold are live. Online reference FCz; acquisition band 0.015–1000 Hz with the hardware notch off; 50 Hz mains. TODO(confirm): the licence is CC BY 4.0 per the data descriptor, but the exact dataset terms are unresolved (§13 item 5).
• Two selections and one honest ugliness. The eyes-closed block was identified algorithmically from the recording’s own marker codes by which code carries more relative occipital alpha, and the channel was chosen as the occipital site with the largest 8–13 Hz share of 1–40 Hz power (O2, ahead of Oz and O1). Because the release has no online high-pass, the segment carries 97.2 µV of slow drift peak-to-peak on a 1-second moving mean against an alpha standard deviation of 6.5 µV; the widget draws the raw and band-passed traces on separate auto-scaled axes and prints both figures rather than filtering the drift away.
• There is a peak to burst. A specparam fit of this exact segment gives an aperiodic exponent of 1.114 with r² = 0.975 and peaks at 10.272 Hz (power 1.27, bandwidth 2.41 Hz), 18.9 Hz and 25.4 Hz, over a 1–40 Hz fit range with max_n_peaks 6, peak_width_limits [1, 8] and min_peak_height 0.1. That is the check this lesson demands, run on the data the lesson uses.
• The spectrum widget serves per-subject spectra and precomputed specparam fits for 12 ds-eegbci subjects at O1, eyes-open and eyes-closed, Welch with 2-s Hann segments, fitted over 1–40 Hz with the settings above. Its compare mode puts two of them side by side with both parameter sets, which is what the exercises below use. All fits are label_source: algorithmic.
• The notebook runs specparam and cycle-by-cycle analysis on ds-lemon eyes-closed data and reports burst rates per subject, so the single-segment numbers above can be seen against a spread.

Explore

Start with the raw trace and the 8–13 Hz band-passed trace side by side: the band-passed trace looks like a continuous rhythm and the envelope above it plainly is not. Now move the threshold from the 50th to the 95th percentile and watch the count, the rate, the mean duration and the duty cycle change while the signal underneath does not — the two numbers the exercises ask for are the ends of that sweep. Set the minimum duration to zero and then to several cycles and watch short crossings appear and disappear. Switch to the 9.5–10.5 Hz narrow preset and see both the trace become more convincingly rhythmic and the filter length — and the contaminated edge — grow.

Put S006 eyes-open beside S006 eyes-closed and read the peak list for each: there is no fitted peak between 8 and 13 Hz in either condition, although the alpha-band power differs between them. Then put S001 eyes-open beside S001 eyes-closed for the contrast — a clear 10 Hz peak appearing as the eyes close. Finally look at S008 eyes-open and ask what its beta peak is worth.

Practice

The notebook fits spectra with specparam and runs cycle-by-cycle analysis on ds-lemon eyes-closed recordings, reporting per-subject peak frequencies, burst rates and duty cycles with the detection rule and its parameters stated in one cell — including which subjects have no fitted alpha peak at all.

Exercises

For the first two, use the widget’s shipped 60-second segment with its defaults: band 8–13 Hz, minimum duration 3 cycles of the band centre, the filter’s contaminated edges excluded, and the threshold set as a percentile of the envelope.