15.2.20  Hann-Poisson window function: hann_poisson_window

The hann_poisson_window command finds a Hann-Poisson window of a sequence.

• hann_poisson_window takes one mandatory argument and two optional arguments:
  • v, a real vector with length n.
  • Optionally, α, a real number (by default 1).
  • Optionally, an interval n₀..n₁ (by default 0..(n−1)).
• hann_poisson_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=

  1 2

  ⎛ ⎜ ⎜ ⎝

  1−cos

  2 k π N−1

  ⎞ ⎟ ⎟ ⎠

  exp

  ⎛ ⎜ ⎜ ⎝

  −

  α |N−1−2 k| N−1

  ⎞ ⎟ ⎟ ⎠

  for k=0,1,…,N−1.

Example.
Input:

Output:

Input:

Output: