### 21.5.10 Parzen window

The parzen_window command applies the Parzen window function to a sequence or its segment.

- parzen_window takes one mandatory argument and two optional arguments:
  - v, a real vector with length n.
  - Optionally, m, N, a sequence of two integers (by default, m=0 and N=n).
- parzen_window returns the elementwise product of [vm,vm+1,…,vm+N−1] and the vector w of length N defined by

  wk=

  ⎧
  ⎪
  ⎪
  ⎨
  ⎪
  ⎪
  ⎩

  1−6xk2 | ⎛ ⎝ | 1−xk | ⎞ ⎠ | ,

  ⎪
  ⎪
  ⎪
  ⎪

  N−1
  2

  −k

  ⎪
  ⎪
  ⎪
  ⎪

  ≤

  N−1
  4

  ,

  2 | ⎛ ⎝ | 1−xk | ⎞ ⎠ | 3,

  otherwise,

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

#### Example

listplot(parzen_window([1$1000]))