Wavelet Analysis of Neuroelectric Waveforms: a Conceptual Tutorial

This paper presents a nontechnical, conceptually oriented introduction to wavelet analysis and its application to neuroelectric waveforms such as the EEG and event related potentials (ERP). Wavelet analysis refers to a growing class of signal processing techniques and transforms that use wavelets and wavelet packets to decompose and manipulate time-varying, nonstationary signals. Neuroelectric waveforms fall into this category of signals because they typically have frequency content that varies as a function of time and recording site. Wavelet techniques can optimize the analysis of such signals by providing excellent joint time-frequency resolution. The ability of wavelet analysis to accurately resolve neuroelectric waveforms into specific time and frequency components leads to several analysis applications. Some of these applications are time-varying filtering for denoising single trial ERPs, EEG spike and spindle detection, ERP component separation and measurement, hearing-threshold estimation via auditory brainstem evoked response measurements, isolation of specific EEG and ERP rhythms, scale-specific topographic analysis, and dense-sensor array data compression. The present tutorial describes the basic concepts of wavelet analysis that underlie these and other applications. In addition, the application of a recently developed method of custom designing Meyer wavelets to match the waveshapes of particular neuroelectric waveforms is illustrated. Matched wavelets are physiologically sensible pattern analyzers for EEG and ERP waveforms and their superior performance is illustrated with real data examples.