### 5.23.10 Bohman window function : bohman_window

bohman_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−xk | ⎞ ⎠ | cos | ⎛ ⎝ | π xk | ⎞ ⎠ | + |
1
π
| sin | ⎛ ⎝ | π xk | ⎞ ⎠ | ,

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

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

followed by scatterplot(L).