> > > Also, I don't believe that it is the case that using the middle slice
> > > affords any greater "accuracy" in making the correction. The slice
> > > correction routine makes the assumption that no meaningful power is present
> > > in the data above the Nyquist frequency. (For which there is some empirical
> > > support). Given this assumption, all shifts in time using
> > sinc-interpolation
> > > are equally valid.
> >
> >I don't think that there are any theoretical reasons why there should not
> >be any power above the Nyquist frequency. A typical HRF to a delta function
> >will contain frequencies higher than the frequency of the acquisition of
> >sucessive scans.
>
> Dear Geoff & John,
> Just another comment/question on sinc-interpolation. When you say
> the routine assumes no meaningful power is present above the Nyquist
> frequency, does this mean you are not doing anything, or do you pre or
> post-filter the data to force it to fit this assumption? When we apply a
> sinc correction to our data, we generally will window the spectrum. If we
> do nothing, a high frequency ringing (sawtooth) will generally be
> introduced into the time series which are shifted due to the small bit of
> high-frequency power. And it will be dependent upon how much it is shifted
> in time. The SPM algorithm (only the one file) I saw doesn't do any
> filtering...but this is probably handled by low-pass filtering downstream I
> assume...eh?
Regarding the band-limited assumption, we only make this
assumnption for the hemodynamic component of the data and not the
entire data. Filtering could not improve the agreement with
this assumption as the assumption concerns the unsampled data and we can
only filter the sampled data.
Regarding your artifact, this would not occur under the
sinc-interpolation/phase-shifting method as the power at the Nyquist
frequency could only be reduced (with an even # of images) or kept the
same (with an odd # of images).
Sincerely,
Eric
Eric Zarahn
University of Pennsylvania
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