# Hann-Poisson window function: hann_poisson_window

### 15.2.20 Hann-Poisson window function: hann_poisson_window

The hann_poisson_window command finds a Hann-Poisson window of a sequence.

- hann_poisson_window takes one mandatory argument and two optional arguments:
  - v, a real vector with length n.
  - Optionally, α, a real number (by default 1).
  - Optionally, an interval n0..n1 (by default 0..(n−1)).
- hann_poisson_window(v ⟨,α,n1..n2⟩) returns the elementwise product of [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.

#### Example.

Input:

L0:=randvector(1000,0..1):;
scatterplot(L0);

Output:

Input:

L:=hann_poisson_window(L0,2):;
scatterplot(L);

Output: