I am wonder how the mentioned program performs the calculation. As long as I know using 3dTproject without -bandpass option will dentrend the signal by a regression using provided vectors and a polynomial order. But, if I use -bandpass option, will the program do the same as above and then filter the frequency? or it applies the filter first and then the regression?

Actually, bandpassing can be done as or inside a regression framework, and this in fact is what the program uses; there is a hint of this at top of the program’s help file:

Note that all the projections are done via linear
regression, including the frequency-based options such as '-passband'. In this
way, you can bandpass time-censored data, and at the same time, remove other
time series of no interest (e.g., physiological estimates, motion parameters).

This is the mathematically consistent/correct way to include both bandpassing and regression-- doing them separately (without other considerations) would not be correct.

So, in short, the answer to your question is that the program does bandpassing and regression simultaneously, because bandpassing can be done as regression.

The
National Institute of Mental Health (NIMH) is part of the National Institutes of
Health (NIH), a component of the U.S. Department of Health and Human
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