Advanced DAX calculation: doing a moving grouped average in PowerPivot

I got an excellent question last week on the ask my answers page that brought me new understanding of DAX. So finally a new interesting (I hope) blog post on DAX.

Let's say I have a set of sales per week of a specific brand:

Now I want to have the average of sales per week (slicable by brand) and compare it to the average of the last 3 weeks. I prepare the pivottable :