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This blog post may assist you a lot with what you're trying to do: Date Comparisons in Tableau Made Easy
I set the parameters as follows
Analysis Type = Rolling Period
Period Type = Days
Period Length = 30
Date Chooser = Custom
Custom Date = 5/25/2015
Further another way to solve what you're after is to use four parameters. One for start of period 1, stop of period 1, start of period 2, stop of period 2, etc.
You can then use your calculations to determine if a date is between any of those intervals and call it your 'current' or 'previous'. However doing this makes it easy to overlap on accident and it requires resetting it each time you want to change a little bit. If you are using the same length periods I would recommend dropping the logic from the above blog post into your workbook.