### 21.5.11 Poisson window

The poisson_window command applies the Poisson window function to a sequence or its segment.

- poisson_window takes one mandatory argument and up to three optional arguments:
  - v, a real vector with length n.
  - Optionally, one of:
    - α, a real number (by default, α=1).
    - m,N⟨,α⟩, a sequence of two integers and optionally a real number α (by default, m=0 and N=n).
- poisson_window returns the elementwise product of [vm,vm+1,…,vm+N−1] and the vector w of length N defined by

  wk=exp

  ⎛
  ⎜
  ⎜
  ⎝

  −α

  ⎪
  ⎪
  ⎪
  ⎪

  2k
  N−1

  −1

  ⎪
  ⎪
  ⎪
  ⎪

  ⎞
  ⎟
  ⎟
  ⎠

  ,k=0,1,…,N−1.

#### Example

listplot(poisson_window([1$1000],2))