### 5.23.12 Gaussian window function : gaussian_window

gaussian_window takes as arguments a real vector v of length n and optionally a positive real number α≤ 0.5 (by default α=0.1 ) 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=exp | ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ | − |
1
2
|  | ⎛ ⎜ ⎜ ⎝ |
k−(N−1)/2
α (N−1)/2
| ⎞ ⎟ ⎟ ⎠ |
2
| ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠

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

L:=gaussian_window(randvector(1000,0..1),0.4):;

followed by scatterplot(L).