### 5.23.8 Blackman-Harris window function : blackman_harris_window

blackman_harris_window takes as arguments a real vector v of length n and optionally 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=a0−a1 cos | ⎛ ⎜ ⎜ ⎝ |
2 k π
N−1
| ⎞ ⎟ ⎟ ⎠ | +a2 cos | ⎛ ⎜ ⎜ ⎝ |
4 k π
N−1
| ⎞ ⎟ ⎟ ⎠ | −a3 cos | ⎛ ⎜ ⎜ ⎝ |
6 k π
N−1
| ⎞ ⎟ ⎟ ⎠

for k=0,1,…,N−1 , where a0=0.35875 , a1=0.48829 , a2=0.14128 and a3=0.01168 . For example, input :

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

followed by scatterplot(L).