### 5.25.17 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).