Dear Greg,

Thank you for the quick reply!

> No further manipulations are performed on the Legendre polynomials in AFNI.
Good to know, then I'll go with the default settings.

> the default cut-off value [...] is purely empirical
Yes. I think it's based on some very old fMRI study which relied on an event-related design, where there should indeed be no/hardly any signal within the slow frequencies. But for block designs removing the noise can likely result in removal of signal, and depending on the design most of the signal might be lost (if it's mainly located within the slow frequencies). Of course one can adjust the cut-off values based on the interval between trials/blocks of the same type (mean? max?), interval plus block length, these two multiplied by factor 2. Or look at the frequency domain plot, but "looking" is very subjective. That's why I've started thinking about polynomials, but actually there are the same issues.

> For example, if the highest-order polynomial coefficient is very small and not statistically significant
With parameter estimates differing from zero and/or statistics reaching significance it would still remain unclear whether the regressor accounts for noise or signal or both. It should be difficult to discern in case of a design for which we expect slow frequency signal. Which brings us back to the question why we go with designs like that in the first place

Best

Helmut