### 21.5.8 Hann-Poisson window

The hann_poisson_window command applies the Hann-Poisson window to a sequence or its segment.

- hann_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).
- hann_poisson_window returns the elementwise product of [vm,vm+1,…,vm+N−1] and the vector w of length N defined by

  wk= |
  1
  2
  |  | ⎛ ⎜ ⎜ ⎝ | 1−cos |
  2 k π
  N−1
  | ⎞ ⎟ ⎟ ⎠ | exp | ⎛ ⎜ ⎜ ⎝ | − |
  α |N−1−2 k|
  N−1
  | ⎞ ⎟ ⎟ ⎠ | , k=0,1,…,N−1.

#### Example

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