### 5.23.21 Welch window function : welch_window

welch_window takes as arguments a real vector v of length n and optionally an interval n1 .. n2 (with default values n1=0 and n2=n−1 ), and returns the elementwise product of the vector [vn1,…,vn2] and the vector w of length N=n2−n1+1 defined by

wk=1− | ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ |
k− |
N−1
2
N−1
2
| ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ |
2

for k=0,1,…,N−1 . For example, input :

L:=welch_window(randvector(1000,0..1)):;

followed by scatterplot(L).