In the case of fMRI the images can be seen as a time series [37] [31]. When the scanning is performed so
fast that the hemodynamic has not reach equilibrium just after a shift in
activation state, the images would represent a smooth curve. Using this
smooth curve as a convolution 
for the time series of a voxel 
we would end up with a ''smooth subtraction image'' (In the case were the
convolution 
is just a ''hard'' on/off switching function in accordance
with the paradigm, we end up with a normal subtraction image).
In the time domain this would be:
The analysis could also be perform in the frequency domain
where 
and 
are the Fourier transformed time series.
Simultaneously fitting the hemodynamic convolution 
would reveal the
dynamics in the brain. Along this road it would be interesting to use a
spatial varying convolution 
This type of analysis has been done by
Lange [37].
If the convolution function is a sinus (cosines), it is equivalent to do a Fourier analysis with just one frequency.
It must be remembered that whatever form one gives the convolution functions, this type of analysis remains voxel-based (if not other techniques is not used to included spatial information).
