Hi, Philipp-

This is the section of the AP help on bandpassing, for reference:
https://afni.nimh.nih.gov/pub/dist/doc/htmldoc/programs/alpha/afni_proc.py_sphx.html#resting-state-note

We should clarify terminology to start:
In resting state FMRI, when people talk about "bandpassing during processing", they are pretty much always referring to low-frequency fluctuation (LFF) bandpassing, to keep only frequencies in a range of approx. 0.01-0.1 Hz. This goes back to early studies and ideas about noise affecting higher frequencies relatively more, as well as possible aliasing of breathing/cardiac effects.
Generally, "bandpassing" means not including either the minimal nor maximal (=Nyquist) frequency in the band range; that is what the LFF range above does. Keeping frequencies 0.0-0.01 Hz would be called "low pass filtering" and keeping 0.01-Nyquist would be "high pass filtering."

There are two main ways to address modeling low frequency drift:
A) exclude the lowest frequencies up to some point---so, a "high pass filter", which in FMRI might be often be frequencies >0.001 Hz or >0.01 Hz.
B) include low-order polynomials in the model---the polort regression you note above, for which the default order chosen by AP depends on the length of the time series, as noted here:

-regress_polort DEGREE  : specify the polynomial degree of baseline

        e.g. -regress_polort 2
        default: 1 + floor(run_length / 150.0)

When time series are very, very long, then the high pass filter might make particular sense, rather than having a very high order polynomial. The AP help notes that quadratic drift is not modeled well by sinusoids, so then the polynomial term would have benefits. In many intermediate cases of not-too-extreme length or drift, the two approaches would likely going to be quite similar.

Note that for every regressor added to your model, you lose a degree of freedom in your output result. For bandpassing, you use 2 regressors per frequency---in standard LFF bandpassing with a TR=2s, this incurs a 60% *loss* in degrees of freedom immediately---censoring and the inclusion of motion and other regressors increases the loss.

The LFF bandpass does two things: exclude some scanner drift, and try to exclude some higher frequencies. In the link at the top, we suggest that the latter part might not always be a good idea---there is a huge statistical cost in terms of degrees of freedom lost, as well as the fact that there is often still much useful information up there.

--pt