Time-Frequency and Oscillations

Level 4 is about what the trial average cannot see. It opens by showing that a burst present on every single trial can be made to vanish from the ERP by letting its phase wander, which is the case for looking at power and phase separately; then it builds the estimators that do that — the short-time Fourier transform and the Morlet wavelet with their fixed uncertainty product, multitaper with a bandwidth you state, filter-Hilbert with a filter you designed — and shows the three disagreeing on the same three seconds of real data. From there: normalizing a map against a baseline, which is where most time-frequency results go wrong, and the event-related desynchronization that is the level’s worked example; the phase itself, intertrial coherence and its small-sample floor, and cross-frequency coupling with the waveform-shape confound that produces it out of nothing; and then the lesson the level exists for.

Two threads run through it. The first is that every number here is a ratio or a smoothing, and both have parameters — cycles, bandwidth, band edges, baseline window, normalization, averaging order, threshold — so a time-frequency result travels with its parameters or it is not a result. The second is stated as a question in L4.6’s title: band power is not the same claim as a rhythm. A band with no spectral peak in it has no rhythm to desynchronize, a narrow filter makes anything look rhythmic, a non-sinusoidal rhythm produces its own harmonics and its own cross-frequency coupling, and a burst count moves by a factor of eleven on a threshold nobody has agreed on. L4.7 is the third stop on the statistics thread that runs from L3.7 through this level to L6.1 and L6.4: the cluster-permutation test is unchanged by a frequency axis, and the discipline needed to use it honestly is not. The capstone puts it together on motor imagery across a documented subset of subjects, including the ones with no mu peak.