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
n
0
..
n
1
(by default 0..(
n
−1)).
gaussian_window(
v
⟨,α,
n
1
..
n
2
⟩
)
returns the elementwise product of [
v
n
1
,…,
v
n
2
] and the vector
w
of length
N
=
n
2
−
n
1
+1 defined by
w
k
=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: