If I understood the question correctly, then this calculated field should do it:
DATEADD('week',-4,[Select Start Date])<=[Start Date]
AND [Start Date] <= [Select Start Date]
The calculation returns True for all Start Dates that are within the specified period, and False for all others.
When you put this field onto the filter shelf, select True and it should work.
And there is no need for the Start Date - 4 Weeks field
Thanks, Dimitri! I was close but couldn't quite get there. Much appreciated!!