I saw the Winograd radix-8 kernel algorithm below, shown in the image. Comparing to the mathematical formula of Cooley-Tukey, there is a multiplication by $\cos$ and $\sin(\pi/8)$, which can't be easily realized by the combinations of $1$ and $\sqrt{1/2}$, which are the components used in Winograd.
• i think there is a typo at the bottom left (regardiing $q(8)$) of the Winograd slide. – robert bristow-johnson Jul 6 '17 at 2:52