based on my tests so far is not just an approximation it's right on the money provided you exclude w n from the window function i'm talking about its magnitude not the unimportant linear phase factor the symmetry issue for n even is also unimportant it only matters for the academic exercise of trying to create a function centered at n whose dtft is real valued but most actual windowing is done like window function window examples with an even number of points and a window centered at n i e the visible peak is flat topped at both w n and w n so the dtft generally has linear phase and therefore is not real valued