How to calculate array by expression with sum, not using loops

I want to calc array (k=1..N) from expression arr(k)=1/N*(\sum_{i=1}^{N}{arr2(i)*cos((2*k-1)*pi*i/N)})
arr2 -- already calculated array
N -- positive integer( it can be very big, so I need solution with good performance)
It is very easy to do with loops, but how to do it without loops?

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