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Yes you can set this up when you create the filter. Drag your date onto the filter shelf, but drag it with the RIGHT mouse button, and it will bring you up some options. Select 'Relative Date' from the options (btw the Right button drag is very handy, and in fact I generally drag all pills this way. eg. if you drag a measure, you'll get options on how you want to aggregate it, rather than just the default). If you then make this a quick filter (and expose on Dashboard) the option will be as per the image you've posted.
Thanks a lot simon