EEG signals are wildly studied to determine how patterns contained within them might reflect control by the nervous system. Generally, they are investigated with frequency analysis based on FFT. However, EEG data sets (including signals in ERP experiments) are non-stationary in both time and space. And FFT is not good at analyzing waveforms with this feature，see this article.
The main advantage of wavelet transform (WT) in the analysis of EEG signals is that it allows accurate decomposition of a neuro-electrical record into a set of component waveforms (detail functions). These detail functions can isolate all scales of waveform structure, from the largest to smallest pattern of variation in time and space that is available in the signal. Consequently WT provides flexible control over the resolution with which different activities and events contained in the neuroelctrical signal can be localized in time, space and scale. This leads to several important applications like(Samar, et al., 1999): (a) noise filtering and signal separation; (b) preprocessing neuroelectric data; (c) neuroelectric signal compressions; (d) spike and transients detections; (e) component and event detection; (f) time-scale and space-scale analysis of neuroelectric waveforms; among others(Rosso, et al., 2006).
Many details have been reviewed by Samar(Samar, et al., 1999).
Rosso, O.A., Martin, M.T., Figliola, A., Keller, K. and Plastino, A. (2006) EEG analysis using wavelet-based information tools, Journal of Neuroscience Methods, 153, 163-182.
Samar, V.J., Bopardikar, A., Rao, R. and Swartz, K. (1999) Wavelet analysis of neuroelectric waveforms: a conceptual tutorial, Brain Lang, 66, 7-60.
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