Dear Pravesh,

These are very good questions. You are right that in the context of "activation" analyses one typically wants to make sure that the high-pass filter does not remove some of your effects of interest so in some scenarios you would want to decrease your high-pass frequency threshold to make sure it encompasses most of your experimental design frequencies (e.g. in a block design if twice your cycle length is above 120s then you would not want to use a 1/120 high-pass threshold because that would remove some of your between-condition main effects, so a lower frequency threshold such as 1/(2*T) might be preferable). In the context of connectivity analyses this is less of a concern, because any potential differences in connectivity between your blocks/conditions are already typically orthogonal to any potential differences in average BOLD signal activation between your blocks/conditions (and the latter are the ones that are affected by high-pass filtering). I have seen argued that for connectivity analyses in block-designs one might want to instead increase the high-pass frequency threshold above .01 (e.g. to 1/L where L is the block length) as a way to focus on within-block fluctuations (vs. between-block fluctuations) in the BOLD signal, yet there is no clear consensus on this and you will find plenty of analysis examples that use different thresholding choices. Personally I would typically use the default .01 threshold for task-related connectivity analyses, but I find other choices perfectly justifiable as well.  

Regarding using different band-pass filter thresholds for different subject groups, this has the potential of creating artifactual differences in connectivity between the groups so I would generally not recommend doing so. The reason is that functional connectivity strength typically varies across different frequency bins (and in a spatially non-homogeneous manner), so comparing the connectivity between two groups that have been differently band-pass filtered is very likely to confound these frequency-specific differences with any true connectivity differences between your groups. In your case, I believe differences in block length between the groups should be a considerably less worrysome source of potential artifactual between-group differences in connectivity than differences in band-pass filter parameters between the groups. If your block lengths are sufficiently large perhaps using a common high-pass threhsold of 1/L (where L is the shortest of the block lengths across the two groups) could be a reasonable way to minimize those differences and make the connectivity results across the two groups most comparable (at the cost of focusing on higher-frequency connectivity effects instead). 

Hope this helps
Alfonso
 
Originally posted by Pravesh Parekh: