resampling

[Christian Hesse]

Hi Sameer,

If you are resampling your data for the purposes of speeding up the
ICA algorithm, then you just take the (de-)mixing matrix and apply to
your original data. Although I would recommend the following
normalization of the mixing matrix (in the following A is the mixing
matrix and W = inv(A) is the de-mixing matrix):

[nchan, nsrcs] = size(A);
for i=1:nsrcs
	A(:,i) = A(:,i)./norm(A(:,i),2);
end
W = inv(A);

this way you ensure that your mixing (and de-mixing) matrix do not
contain information about the power of the components but merely
about spatial projections (and the spatial correlations of these), so
that when you apply W to your data (at the original sampling rate),
you can treat the variance (power) of the components s = Wx as
"correct".

Some further comments to bear in mind: since in estimating the ICA on
the downsampled data you in effect assume that the high-frequency
content (above the Nyquist limit of your resampling frequency) is not
relevant. Hence you might as well continue working with the
downsampled data. However, if there IS stuff going on in the high-
frequency bands that is important (e.g., part of a string artifact
signal which has a broad band spectrum), then the ICA model estimated
on the downsampled data will effectively be "wrong" and will not be
able to successfully separate your data into independent components.
This may be an unlikely scenario for very high frequencies, but the
considerations should guide you in choosing a resampling rate that is
not "too low".

Regards,
Christian


On 22 Feb 2007, at 18:29, Sameer Walawalkar wrote:

> Hello,
>
> How exactly does resampling work? If I resample data to 300 Hz from
> 1KHz, will the resulting data structure have encoded information
> for going back to 1KHz?
>
> This is so that I could resample down, do ICA, remove components,
> and then get back to 1KHz. (Clearly, I dont understnad the
> resampling algorithm).
>
> thanks,
> sameer
>

----------------------------------------------------------------------
Christian Hesse, PhD, MIEEE

F.C. Donders Centre for Cognitive Neuroimaging
P.O. Box 9101
NL-6500 HB Nijmegen
The Netherlands

Tel.: +31 (0)24 36 68293
Fax: +31 (0)24 36 10989

Email: c.hesse at fcdonders.ru.nl
Web: www.fcdonders.ru.nl
----------------------------------------------------------------------




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