### 5.23.7 Bartlett-Hann window function : bartlett_hann_window

bartlett_hann_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 | ⎪ ⎪ ⎪ ⎪ |
k
N−1
| − |
1
2
| ⎪ ⎪ ⎪ ⎪ | −a2 cos | ⎛ ⎜ ⎜ ⎝ |
2 k π
N−1
| ⎞ ⎟ ⎟ ⎠

for k=0,1,…,N−1 , where a0=0.62 , a1=0.48 and a2=0.38 . For example, input :

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

followed by scatterplot(L).