Dear Donald,
I didn't want to argue against HPF or other methods, I just wanted to stress that some of the papers on HPF do not go into detail about what their results really mean for a "default" GLM analysis, or rephrased and more precisely, I would be interested to see these analyses performed on smoothed data as well.
Concerning low frequencies and "noise", it's always good to keep in mind that it's an oversimplification, as within a certain experiment, it might always be a correlate of some neural process, e.g. possibly also related to performance changing over time. It's just that usually we don't want to look at these effects, as we prefer constant activations over time, leaving aside whether this assumption makes sense at all. I was in the scanner many times with many different paradigms, but after some time, say 20 min, I always start to feel a little different, e.g. uncomfortable/bored/sleepy/whatever, and I would be surprised if this had no impact on BOLD data. Alternatively, some experiments are explicitely interested in changes over time but when looking at their methods section and the paradigm you will notice that effectively, they removed this part of the signal.
A while ago I ran some analyses without the DCT and just two regressors modeling linear and quadratic changes just to see how the beta estimates would look like. I was surprised to find robust "activations" within and across subjects restricted to well-specified functional brain regions. Thus, they clearly did not (just) model drift but also some change in activation over time, although people usually agree that linear changes mainly reflect drift.
Best
Helmut
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