Parzen window

### 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= |
  ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ |
  1−6 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

listplot(parzen_window([1$1000]))