Gaussian window function

### 19.5.6 Gaussian window function

The gaussian_window command applies the Gaussian window function to a sequence or its segment.

- gaussian_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 not larger than 0.5 (by default, α=0.1).
    - m,N ⟨,α⟩, a sequence of two integers and optionally a real number α≤ 0.5 (by default, m=0 and N=n).
- gaussian_window returns the elementwise product of [vm,vm+1,…,vm+N−1] and the vector w of length N defined by

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

#### Example

listplot(gaussian_window([1$1000],0.4))