Wavelet analysis of EEGs

[crosley at tcp.co.uk]

     20/Nov/97
     A  thank  you to those who responded to  my  request  of
     28/9/97  for  information on Wavelet Analysis.  At  that
     time I wrote :

     > Can anyone suggest an introductionn to wavelet
     >  analysis with no, or minimum maths? I have Hubbard's
     >  book but find it a bit obtuse. I am particularly
     >  interested in EEG applications.

     The  most  useful info was probably an  introduction  to
     Robi      Polikar's      Wavelet      Tutorial       at:
     www.public.iastate.edu/~rpolikar/wavelet.html

     I  am  a  retired EEG researcher still  writing  on  EEG
     matters  and currently writing a contribution on  recent
     trends  in  EEG  analysis  for a  new  EEG  book  to  be
     published  next year.  Therefore I wanted to  understand
     the  concepts  rather than how to do the  analysis.   My
     maths is a bit rusty,  although in the past I have  done
     original work on EEG coherence analysis.

     On  the whole EEGers are not mathematics  sophisticates,
     although  they may understand the principles of  Fourier
     and spectral analysis because frequency is an  important
     part  of  EEG analysis and  interpretation.  They  would
     understand   that   basic  wavelet   analysis   involves
     correlating  a frequency band limited waveform with  the
     EEG signal at various time displacements throughout  the
     signal and for various frequency bands.  But not if this
     was just expressed mathematically.  I think I have  only
     seen  one  paper describing wavelet  analysis  in  these
     terms.   Usually  it  is  wrapped  up  in  the  sort  of
     mathematics  that would frighten off EEG clinicians.  On
     that theme, Kaiser's book would probably be very good if
     one had the time to digest it,  but most clinical EEGers
     just don't.  They would be put off by the high ratio  of
     formulae to text.

     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.