# Blackman-Harris window function: blackman_harris_window

### 15.2.14 Blackman-Harris window function: blackman_harris_window

The blackman_harris_window command finds a Blackman-Harris window of a sequence.

- blackman_harris_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)).
- blackman_harris_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 cos

  ⎛
  ⎜
  ⎜
  ⎝

  2 k π
  N−1

  ⎞
  ⎟
  ⎟
  ⎠

  +a2 cos

  ⎛
  ⎜
  ⎜
  ⎝

  4 k π
  N−1

  ⎞
  ⎟
  ⎟
  ⎠

  −a3 cos

  ⎛
  ⎜
  ⎜
  ⎝

  6 k π
  N−1

  ⎞
  ⎟
  ⎟
  ⎠

  for k=0,1,…,N−1, where a0=0.35875, a1=0.48829, a2=0.14128 and a3=0.01168.

#### Example.

Input:

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

Output:

Input:

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

Output: