# Bohman window function: bohman_window

### 15.2.16 Bohman window function: bohman_window

The bohman_window command finds a Bohman window of a sequence.

- bohman_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)).
- bohman_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−xk

  ⎞
  ⎠

  cos

  ⎛
  ⎝

  π xk

  ⎞
  ⎠

  +

  1
  π

  sin

  ⎛
  ⎝

  π xk

  ⎞
  ⎠

  ,

  where xk=|2 k/N−1−1| for k=0,1,…,N−1.

#### Example.

Input:

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

Output:

Input:

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

Output: