It is possible to implement a fourier analysis in the form of a General
Linear Model. As Jack mentioned, there will be correlation between a
set of time-lagged cosine functions.
However, a sine and cosine will be uncorrelated and the combination of
these regressors can be used to encode the phase of the stimulus (thank
you to Oliver Josephs).
i.e. sin(wt + theta) = cos(theta)sin(wt) + sin(theta)cos(wt)
= B1 sin(wt) + B2 cos(wt),
where:
B1 = cos(theta)
B2 = sin(theta).
Since:
tan(theta) = sin(theta)/cos(theta)
Then, (and using a built-in Matlab function),
theta = atan2(B2, B1)
w = frequency of stimulus (e.g. units: 2*pi/scans)
t = time (e.g. units scans)
theta = phase offset (e.g. units radians)
B1, B2 = SPM parameter estimates
The way we have done this in SPM is to use the "imcalc" button to calculate
the inverse tan of the two beta images (one representing the parameter
estimates for the sine covariate and the other for the cosine). The
result *should be* an image where grey level maps to phase angle.
Chloe
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Chloe Hutton
Wellcome Department of Cognitive Neurology
Institute of Neurology
12 Queen Square
London WC1N 3BG
[log in to unmask]
http://www.fil.ion.ucl.ac.uk
Tel: +44 (0)20 7833-7487 (direct)
+44 (0)20 7833-7472
Fax: +44 (0)20 7813-1420
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