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21: Wavelet
In wavelet transformation, a wavelet can be considered similar to a frequencyselective
“window” that is convolved (shifted) along a signal in the time domain to
determine the degree to which the frequency content of the signal corresponds to that
of the wavelet.
The convolution reveals the magnitude of the correspondence, which is represented
by the wavelet coefficient. Magnitude is indicated by units of power (which is
amplitude squared). A high wavelet coefficient indicates a high correspondence
between the frequencies measured by the wavelet and the frequencies contained in a
localized section of the signal. A low coefficient indicates a low correspondence.
(The wavelet coefficient also provides information about phase stability, which
indicates whether activity is correlated across trials; this is described further in
Chapter 12, “Wavelet Display,” in the Net Station Viewer Technical Manual.)
Compressing or dilating the wavelet in time creates other members of the wavelet
family, enabling you to adjust the frequency selectivity of the wavelet. Compressed
wavelets measure higher frequencies; dilated wavelets measure lower frequencies.
Each member of the wavelet family is convolved with the EEG signal in the time
domain to determine the presence of other frequency ranges.
Note: In the frequency domain, a wavelet is in effect a bandpass filter, and a series of
wavelets is similar to a filter bank.
In essence, we are filtering different frequency bands, cutting these bands into slices
in time, and analyzing their energy content. The result is a signal whose frequency
content is localized in time by the values of its wavelet coefficients; the wavelet
coefficients for each position and frequency of the scaled wavelets can be plotted on
a graph. Net Station displays this information in the Wavelet Display (see the
Net Station Viewer Technical Manual).
Resources for newcomers to wavelets include:
• Graps, A. (1995–2004). Amara’s wavelet page. Retrieved from http://
www.amara.com/current/wavelet.html
• Herrmann, C.S., Grigutsch, M., & Busch, N.A. (2005). EEG oscillations and
wavelet analysis. In T.C. Handy (Ed.), Event-related potentials: A methods
handbook (pp.229–259). Cambridge: MIT Press.
• Valens, C. (1999). A really friendly guide to wavelets. Retrieved from http://
perso.wanadoo.fr/polyvalens/clemens/wavelets/wavelets.html
192 Net Station Waveform Tools Technical Manual S-MAN-200-WFTR-001 • December 21, 2006