High-pass filtering is often used in neuroimaging data analysis. Commonly, whenever a general linear model is fitted to the data (as for instance in statistic parametric mapping) a number of columns of the design matrix are assigned to discrete cosines (DC). See the figure below for a graphical example.
I am curious why this is preferred to taking the fourier transform (FT) of the data, and applying a filter or cutoff. Arguments I think would speak for the FT alternative are:
- You would not have to re-do the high-pass filtering upon every application of a GLM
- Since DCT is discrete I am guessing a FT would be more accurate in extracting all high frequeny components (looking at the figure above, I find it hard to believe that those few cosines cover all the low-frequency spectrum in between them)
Reasons I think DCT might be the preferred method:
- Maybe it is faster than FFT.
- Maybe there is a reason why it is desirable to perform the filtering concomitantly with your GLM fitting.
Could you tell me what you think about this?
- Why is DCT preferred?
- Would FFT not be better?