# Triangular window function: triangle_window

### 15.2.25 Triangular window function: triangle_window

The triangle_window command finds a triangle window of a sequence.

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

  wk=1−

  ⎪
  ⎪
  ⎪
  ⎪
  ⎪
  ⎪
  ⎪

  n−

  N−1
  2

  N+d
  2

  ⎪
  ⎪
  ⎪
  ⎪
  ⎪
  ⎪
  ⎪

  for k=0,1,…,N−1.

The case d=−1 is called the Bartlett window function.

#### Example.

Input:

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

Output:

Input:

L:=triangle_window(L0,1):;
scatterplot(L);

Output: