15.2.22  Parzen window function: parzen_window

The parzen_window command finds a Parzen window of a sequence.

• parzen_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)).
• parzen_window(v ⟨,n₁..n₂⟩) returns the elementwise product of [v_n1,…,v_n2] and the vector w of length N=n₂−n₁+1 defined by

  wk=	⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩      ⎛ ⎝ 1−6 xk2  ⎛ ⎝ 1−xk ⎞ ⎠ ⎞ ⎠ , ⎪ ⎪ ⎪ ⎪ N−1 2 −k ⎪ ⎪ ⎪ ⎪ ≤ N−1 4 ,     2  ⎛ ⎝ 1−xk ⎞ ⎠ 3, otherwise,

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

Example.
Input:

Output:

Input:

Output: