# Poisson window function: poisson_window

### 15.2.23 Poisson window function: poisson_window

The poisson_window command finds a Poisson window of a sequence.

- 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)).
- 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=exp

  ⎛
  ⎜
  ⎜
  ⎝

  −α

  ⎪
  ⎪
  ⎪
  ⎪

  2 k
  N−1

  −1

  ⎪
  ⎪
  ⎪
  ⎪

  ⎞
  ⎟
  ⎟
  ⎠

  for k=0,1,…,N−1.

#### Example.

Input:

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

Output:

Input:

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

Output: