# Bartlett-Hann window function: bartlett_hann_window

### 15.2.13 Bartlett-Hann window function: bartlett_hann_window

The bartlett_hann_window command finds a Bartlett-Hahn window of a sequence, which can be used to examine a short segment when analyzing a long.

- bartlett_hann_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)).
- bartlett_hann_window(v ⟨,n1..n2⟩) returns the elementwise product of [vn1,…,vn2] and the vector w of length N=n2−n1+1 defined by

  wk=a0+a1

  ⎪
  ⎪
  ⎪
  ⎪

  k
  N−1

  −

  1
  2

  ⎪
  ⎪
  ⎪
  ⎪

  −a2 cos

  ⎛
  ⎜
  ⎜
  ⎝

  2 k π
  N−1

  ⎞
  ⎟
  ⎟
  ⎠

  for k=0,1,…,N−1 , where a0=0.62 , a1=0.48 and a2=0.38 .

#### Example.

Input:

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

Output:

Input:

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

Output: