Poisson window function

### 19.5.11 Poisson window function

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

- poisson_window takes one mandatory argument and one 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 | ⎪ ⎪ ⎪ ⎪ |
  2 k
  N−1
  | −1 | ⎪ ⎪ ⎪ ⎪ | ⎞ ⎟ ⎟ ⎠ | , k=0,1,…,N−1.

#### Example

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