Gaussian window function: gaussian_window

### 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 [vn1,…,vn2] 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:

L0:=randvector(1000,0..1):;
scatterplot(L0);

Output:

Input:

L:=gaussian_window(L0,0.4):;
scatterplot(L);

Output: