Power-of-Cosine Window Family

Definition:

$$w(n)=w_R(n) \cos^P\left( \frac{ \pi n}{M} \right)$$ (4.29)

where $P$ is a nonnegative integer.

Properties:

• The first $P$ terms of the window's Taylor expansion, evaluated at the endpoints are identically 0 .
• Roll-off rate $\approx 6(P+1)$ dB/octave.

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.