# Welch window function: welch_window

### 15.2.27 Welch window function: welch_window

The welch_window command finds a Welch window of a sequence.

- welch_window takes one mandatory argument and one optional argument:
  - v, a real vector with length n.
  - Optionally, an interval n0..n1 (by default 0..(n−1)).
- welch_window(v ⟨,n1..n2⟩) returns the elementwise product of [vn1,…,vn2] and the vector w of length N=n2−n1+1 defined by

  wk=1−

  ⎛
  ⎜
  ⎜
  ⎜
  ⎜
  ⎜
  ⎝

  k−

  N−1
  2

  N−1
  2

  ⎞
  ⎟
  ⎟
  ⎟
  ⎟
  ⎟
  ⎠

  2

  for k=0,1,…,N−1.

#### Example.

Input:

L0:=randvector(1000,0..1):;
scatterplot(L0);

Output:

Input:

L:=welch_window(L0):;
scatterplot(L);

Output: