Parzen window function: parzen_window

### 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 [vn1,…,vn2] 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 xk=|1−2 k/N−1| for k=0,1,…,N−1.

Example.
Input:

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

Output:

Input:

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

Output: