Window Transform:

$$W_{BH}(\omega) = \sum_{k=-(L-1)}^{L-1}\alpha_k W_R(\omega + k\Omega_M)$$

where $W_R(\omega) = M\cdot\hbox{asinc}_M(\omega)$ denotes the rectangular-window transform, and $\Omega_M = 2\pi/M$.

Note that for $L=1$, we obtain the rectangular window, and for $L=2$, the BH family specializes to the generalized Hamming family.