### 5.23.18 Riemann window function : riemann_window

riemann_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
| ,
sin(π xk)
π xk
| ,
| otherwise,

where xk=2 k/N−1−1 , for k=0,1,…,N−1 . For example, input :

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

followed by scatterplot(L).