15.2.18  Gaussian window function: gaussian_window

The gaussian_window command finds a Gaussian window of a sequence.

• gaussian_window takes one mandatory argument and two optional arguments:
  • v, a real vector with length n.
  • Optionally, α, a real number less than or equal to 0.5 (by default 0.1).
  • Optionally, an interval n₀..n₁ (by default 0..(n−1)).
• gaussian_window(v ⟨,α,n₁..n₂⟩) returns the elementwise product of [v_n1,…,v_n2] and the vector w of length N=n₂−n₁+1 defined by

  wk=exp

  ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝

  −

  1 2

  ⎛ ⎜ ⎜ ⎝

  k−(N−1)/2 α (N−1)/2

  ⎞ ⎟ ⎟ ⎠

  2

  ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠

  for k=0,1,…,N−1.

Example.
Input:

Output:

Input:

Output: