Special Cases:

• $P=0 \Rightarrow$ Rectangular window
• $P=1 \Rightarrow$ MLT sine window
• $P=2 \Rightarrow$ Hann window (``raised cosine'' = ``$\cos^2$'')
• $P=4 \Rightarrow$ Alternative Blackman (maximized roll-off rate)

Thus, $\cos^P$ windows parametrize $L$-term Blackman-Harris windows (for $L=P/2+1$) which are configured to use all degrees-of-freedom to maximize roll-off rate.