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.