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 [v_m,v_m+1,…,v_m+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 x_k=|1−2 k/N−1| for k=0,1,…,N−1.

Example