Many EEG effects are not visible in an averaged waveform, because they are oscillatory changes that are not phase-locked to the event: mu suppression during motor imagery, alpha changes with attention, beta rebound after movement. Time-frequency analysis estimates power and phase at each frequency over time, trial by trial, and then averages, so non-phase-locked activity survives.
Two quantities come out of it. Event-related spectral perturbation (ERSP) is the change in power relative to a baseline, usually in dB. Inter-trial coherence (ITC) is how consistent the phase is across trials at each time and frequency. It is high for evoked, phase-locked responses and low for induced ones.
Decomposition methods
BCILattice's Time-Frequency step offers all three, computes the decomposition once, and caches it. Channel, class, band preset, response window and significance masking are view controls that redraw from the cache rather than recomputing.
| Method | Strength | Trade-off |
|---|---|---|
| Morlet wavelet | Time resolution that adapts with frequency | Number of cycles trades time against frequency precision |
| STFT | Simple and fast, fixed window | Same resolution at every frequency |
| Multitaper | Low-variance spectral estimates, good for higher frequencies | Smears in frequency by design |
Seven views of one computation
Overview
ERSP and ITC for one channel on a shared time axis, with frequency marginals and per-band time courses.
Channel Grid
Every channel's ERSP on one shared colour scale: the spatial layout of the effect.
Summary
Peak ERD/ERS in dB, peak time, peak frequency, mean dB, mean and peak ITC, per class and band. These are the numbers you quote in a paper, and they export as CSV.
Significance
"Mask non-significant" outlines bins belonging to a significant cluster from a one-sample cluster-permutation test against 0 dB at p < 0.05.
Why cluster permutation
A time-frequency map has thousands of bins, and testing each one separately guarantees false positives. Cluster-based permutation testing groups adjacent significant bins into clusters and compares cluster size against a null distribution built by permutation, controlling the error rate across the whole map without assuming independent bins.
A limit worth knowing for fNIRS
The haemodynamic response lives below about 0.1 Hz, and at fNIRS sampling rates a wavelet decomposition has limited resolution there. Time-frequency peaks in the fNIRS band read roughly 30% low in our measurements. This is a property of the method, and the documentation states it.
Questions
What is ERSP in EEG?
Event-related spectral perturbation is the change in spectral power at each time and frequency relative to a pre-stimulus baseline, usually expressed in dB and averaged over trials.
What is inter-trial coherence (ITC)?
ITC measures how consistent the phase of an oscillation is across trials at each time and frequency, from 0 (random phase) to 1 (identical phase). High ITC indicates an evoked, phase-locked response.
Morlet wavelet or STFT for EEG?
Morlet wavelets are the usual choice because time resolution improves at higher frequencies. STFT is simpler with a fixed window. Multitaper suits higher-frequency power estimates.
How do I test time-frequency results for significance?
Use a cluster-based permutation test, which controls false positives across the whole time-frequency map instead of testing each bin separately.
Read the reference
Related
EEG Frequency Bands: Delta, Theta, Alpha, Beta, Gamma
EEG is described in frequency bands, from slow delta to fast gamma. The bands are a useful shorthand for a continuous spectrum, and the popular "one wave, one mental state" story oversimplifies them.
Motor Imagery BCI: EEG Classification Explained
Imagining a movement suppresses the mu and beta rhythms over the opposite motor cortex. A motor imagery BCI detects that suppression and turns it into a command, with no movement and no external stimulus.
EEG Feature Extraction: Which Features to Use
A feature is a reduction of a trial to a number. The right ones depend on where the signal lives (time, frequency, space or the links between channels), and the wrong ones multiply until the model overfits.
EEG Connectivity Analysis: Coherence, PLV, PLI, wPLI
Connectivity measures ask whether two EEG channels behave as if their sources interact. At the scalp, the first thing to rule out is that they are measuring the same source.