### 5.23.9 Blackman window function : blackman_window

blackman_window takes as arguments a real vector v of length n and optionally a real number α (by default α=0.16 ) and/or an interval n1 .. n2 (with default values n1=0 and n2=n−1 ), and returns the elementwise product of the vector [vn1,…,vn2] and the vector w of length N=n2−n1+1 defined by

wk= |
1−α
2
| − |
1
2
| cos | ⎛ ⎜ ⎜ ⎝ |
2 k π
N−1
| ⎞ ⎟ ⎟ ⎠ | + |
α
2
| cos | ⎛ ⎜ ⎜ ⎝ |
4 k π
N−1
| ⎞ ⎟ ⎟ ⎠

for k=0,1,…,N−1 . For example, input :

L:=blackman_window(randvector(1000,0..1)):;

followed by scatterplot(L).