### 5.23.14 Hann-Poisson window function : hann_poisson_window

hann_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= |
1
2
|  | ⎛ ⎜ ⎜ ⎝ | 1−cos |
2 k π
N−1
| ⎞ ⎟ ⎟ ⎠ | exp | ⎛ ⎜ ⎜ ⎝ | − |
α |N−1−2 k|
N−1
| ⎞ ⎟ ⎟ ⎠

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

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

followed by scatterplot(L).