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When
in (3.26), we obtain the Blackman family:

(4.28) 
Relative to the generalized Hamming family (§3.2), we
have added one more cosine weighted by
. We now therefore
have three degrees of freedom to work with instead of two. In
the Hamming family, we used one degree of freedom to normalize the
window amplitude and the second was used either to maximize rolloff
rate (Hann) or sidelobe rejection (Hamming). Now we can use two
remaining degrees of freedom (after normalization) to optimize these
objectives, or we can use one for each, resulting in three subtypes
within the Blackman window family.
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