### 5.23.17 Poisson window function : poisson_window

poisson_window takes as arguments a real vector v of length n and optionally a real number α (by default α=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 | ⎛ ⎜ ⎜ ⎝ | −α | ⎪ ⎪ ⎪ ⎪ |
2 k
N−1
| −1 | ⎪ ⎪ ⎪ ⎪ | ⎞ ⎟ ⎟ ⎠

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

L:=poisson_window(randvector(1000,0..1),2):;

followed by scatterplot(L).