### 5.23.19 Triangular window function : triangle_window

triangle_window takes as arguments a real vector v of length n and optionally an integer d∈{−1,0,1} (by default d=0 ) and/or 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− | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ |
n− |
N−1
2
N+d
2
| ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪

for k=0,1,…,N−1 (the case d=−1 is called the Bartlett window function). For example, input :

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

followed by scatterplot(L).