### 21.5.15 Welch window

The welch_window command applies the Welch window function to a sequence or its segment.

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

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

#### Example

listplot(welch_window([1$1000]))