21.5.14  Tukey window

The tukey_window command applies the Tukey window function to a sequence or its segment.

• tukey_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 in [0,1] (by default, α=0.5).
    • m,N ⟨,α⟩, a sequence of two integers and optionally a real number α∈[0,1] (by default, m=0 and N=n).
• tukey_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 2   ⎛ ⎜ ⎜ ⎝ 1+cos ⎛ ⎜ ⎜ ⎝ π  ⎛ ⎜ ⎜ ⎝ k β −1 ⎞ ⎟ ⎟ ⎠ ⎞ ⎟ ⎟ ⎠ ⎞ ⎟ ⎟ ⎠ , k<β,       1, β≤ k≤(N−1)  ⎛ ⎜ ⎜ ⎝ 1− α 2 ⎞ ⎟ ⎟ ⎠ ,        1 2   ⎛ ⎜ ⎜ ⎝ 1+cos ⎛ ⎜ ⎜ ⎝ π  ⎛ ⎜ ⎜ ⎝ k β − 2 α +1 ⎞ ⎟ ⎟ ⎠ ⎞ ⎟ ⎟ ⎠ ⎞ ⎟ ⎟ ⎠ , otherwise,

  where β=α (N−1)/2, for k=0,1,…,N−1.

Example