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Wavelet analysis of EEGs

Hansjerg Gölz hgo14 at elec.canterbury.ac.nz
Mon Nov 24 21:13:05 EST 1997

In article <NEWTNews.880038457.3239.crosley at crosley.tcp.co.uk>,
  crosley at tcp.co.uk wrote:
>      All of which is a preamble to a further request.  I need
>      a  diagram which illustrates wavelet analysis of an  EEG
>      without any frills.  I see this as a diagram like figure
>      1 of M.  Akay (1995) Wavelets in Biomedical Engineering,
>      Annals of Biomedical Engineering; 23: 531-542,  but with
>      an  epoch  of EEG instead of the ECG shown  there.  This
>      shows  an  ECG  signal with below a  series  of  wavelet
>      analyses at differing dilations.  For EEGers it would be
>      preferable if the x-axis is time as it is there and  not
>      translation as it often is. Also the y-axis scale should
>      be frequency bands rather than dilation.
>      Can anyone help?
>      If  all  of  this says I have got it  wrong  about  what
>      wavelet analysis does, please enlighten me! John Shaw.

Hi John,

I calculated the Continuous Wavelet Transform (CWT) for a
10 s EEG bipolar trace (channel C4-P4, sampled at 200 Hz)
using the wavelet  described by  Senhadji et al [1]  with
parameter k=7. An short oscillation in the beta range
(could be due to a movement artifact) can be observed near
the center of the temporal interval [2]. The x-axes are
scaled to samples (aligned between plots), the upper
y-axes shows microvolts while the lower one shows Hertz.

The wavelet function is complex valued, thus the CWT is
complex valued as well. Only the magnitudes (absolute
values) of the coefficients are shown here. Although a
complex wavelet may be more complicated to understand
(exp. from the EEGers point of view) the resulting CWT
is more straightforward (it shows no 'phase throughs').

Cheers, Hansjerg

[1]  Senhadji,L., Dillenseger,J.L., Wendling, F., Rocha,C.
and Kinie,A. (1995), 'Wavelet analysis of EEG  for
three-dimensinal mapping  of epileptic events.'
Annals of Biomedical Engineering, vol. 23, pp. 543-552.

[2] http://www.mathematik.uni-marburg.de/~hangi/beta.jpg

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