Event-related potentials and oscillations

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Averaging keeps what is locked

Add fifty epochs, each aligned to its stimulus, and divide by fifty. Anything with the same shape and timing on every trial survives. Anything with random timing, or random sign, shrinks toward zero at a rate of one over the square root of the number of trials. The survivor is the ERP. Its named bumps are called components: P1, N1, P2 (early sensory), N170 (faces), P300 (rare targets), N400 (semantic surprise), the ERN (errors), each with a typical latency, polarity, and scalp location.

Averaging assumes the response is the same every time. It is not, quite; latency jitters from trial to trial, which smears the average and makes fast components look smaller. That is a limitation to know about, not a reason to stop averaging.

Oscillations change in power and phase

Alpha does not have a fixed shape locked to anything; it waxes and wanes on its own schedule. Averaging the raw signal across trials cancels it, because its phase differs on every trial. To see it, compute power (square the band-passed signal, or take the spectrogram) on each trial first, then average the power. Now a rhythm that reliably gets weaker after a movement cue shows up as a dip in mu power, the event-related desynchronizationEvent-related desynchronization (ERD)The drop in rhythmic power over a cortical area when it becomes active, such as mu weakening when you imagine moving your hand. Glossary entry, even though the raw average shows nothing.

So: average the signal to see ERPs; average the power to see oscillatory changes. Doing the wrong one shows nothing and leads people to conclude there is nothing.

Time-frequency analysis

The spectrogramSpectrogramA spectrum computed over sliding windows and plotted against time, showing how frequency content changes. Glossary entry or the wavelet transformWavelet transformA time-frequency analysis that uses short wiggles at high frequencies and long ones at low, matching the trade-off to the frequency. Glossary entry, applied per trial and averaged, gives a picture with time along the bottom, frequency up the side, and colour for power relative to baseline. ERD appears as a blue patch in the mu band during movement. A rebound of beta after movement appears red. Gamma bursts during attention appear, weakly, and often turn out to be muscle. The trade the spectrum page described holds: short windows for time, long for frequency, and wavelets adjust the window to the frequency automatically.

Phase

Beyond power, oscillations have phase, and phase carries information. Inter-trial phase coherence measures whether a rhythm’s phase is consistent across trials at each time; a strong value right after a stimulus means the stimulus reset the rhythm. Phase-locking between two channels measures whether two regions oscillate in step, which is the most common (and most over-interpreted) measure of “connectivity.” And an ERP can itself be thought of as a phase reset of ongoing rhythms; the debate over whether that is what ERPs are has run for twenty years.

Where decoders live

P300 spellers decode an ERP: the classifier looks at the average-like shape of each epoch. Motor imagery decodes oscillations: the classifier looks at band power over channels. SSVEP decodes a driven oscillation: the classifier looks for a frequency. Knowing which language your paradigm speaks tells you what features to extract and what preprocessing will destroy the signal. High-pass at 1 Hz kills slow ERPs; averaging raw signal kills induced responses.