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 [v_n1,…,v_n2] 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:

Output:

Input:

Output: