a triangular (bartlett) window has a kink (discontinuity in first derivative). thinking in the continuous (not discrete) case, my intuition is that the fourier transform of any window with a kink must asymptote to a non-zero value (rather than exponentially decay), since it should take infinitely high frequencies to be able to sum to a precisely sharp "corner." treated as the kernel (impulse response) of a filter, this would correspond to passing arbitrarily high frequencies.
is this right? in general, how do i calculate the asymptotic value, and why isn't this a standard quoted feature of a window?