I was looking at this as well and came up with a solution in Advanced Report Builder that is a bit more automated than what is suggested above. I still need to run this next week to be sure, but it appears to pull the Friday of the previous week.
In the header of my report, I have a standard text field: 'Week Ending '
Next to that I inserted a Query Calculation Object, and named it 'theDate'.
In the Expression Definition, I entered:
_add_days(current_date,-1*(_day_of_week(current_date,6)))
This basically says to go to subtract x number of days from the current date. I have this set for Friday, but if I wanted Sunday, for example, I'd change the 6 to an 8.
Again, I need to check this next week, but it should be a right start, anyway. 
UPDATE: Checked this week and it functions as intended. I finally get to automate the sending of these reports!