Time-frequency microstructure and statistical significance of ERD and ERS

ERD and ERS were introduced as the time courses of the average changes of energy in given frequency bands. These curves are naturally embedded in the time-frequency plane. Time-frequency density of signals energy can be estimated by means of a variety of transforms. In general, resolution of these methods depends on a priori choices of parameters regulating the tradeoff between the time and frequency resolutions. As an exception, adaptive time-frequency approximations adapt resolution to the local structures of the analyzed signal. Matching pursuit (MP) algorithm is a reliable implementation of this approach. Its application to the event-related EEG allows for a detailed presentation of the time-frequency microstructure of changes of the average energy density, as well as calculation of high-resolution maps of ERD/ERS in the time-frequency plane. However, even with such a detailed picture of the signal energy changes, their significance remains an open issue. Owing to a stochastic character of the EEG, a visible increase or decrease of energy can occur due to a pure chance or a phenomenon unrelated to the event. For a proper estimation of the statistical significance of ERD/ERS, that is, the average changes of signals energy density in relation to the reference period, we must take into account possibly non-normal distributions of energy, and, especially, the problem of multiple comparisons appearing in hypotheses related to different frequency bands and time epochs. This chapter presents and discusses a complete framework for high-resolution estimation of the ERD/ERS microstructure in the time-frequency regions, revealing statistically significant changes.