21.5.6  Gaussian window

The gaussian_window command applies the Gaussian window function to a sequence or its segment.

• gaussian_window takes one mandatory argument and up to three optional arguments:
  • v, a real vector with length n.
  • Optionally, one of:
    • α, a real number not larger than 0.5 (by default, α=0.1).
    • m,N ⟨,α⟩, a sequence of two integers and optionally a real number α≤ 0.5 (by default, m=0 and N=n).
• gaussian_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=exp

  ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝

  −

  1 2

  ⎛ ⎜ ⎜ ⎝

  k−(N−1)/2 α (N−1)/2

  ⎞ ⎟ ⎟ ⎠

  2

  ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠

  ,    k=0,1,…,N−1.

Example