# Riemann window function: riemann_window

### 15.2.24 Riemann window function: riemann_window

The riemann_window command finds a Riemann window of a sequence.

- riemann_window takes one mandatory argument and one optional argument:
  - v, a real vector with length n.
  - Optionally, an interval n0..n1 (by default 0..(n−1)).
- riemann_window(v ⟨,n1..n2⟩) returns the elementwise product of [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.

#### Example.

Input:

L0:=randvector(1000,0..1):;
scatterplot(L0);

Output:

Input:

L:=riemann_window(L0):;
scatterplot(L);

Output: