Parzen window function : parzen

5.27.22 Parzen window function : parzen_window

parzen_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 [v_n₁,…,v_n₂] and the vector w of length N=n₂−n₁+1 defined by

w_k=

⎧
⎪
⎪
⎨
⎪
⎪
⎩

⎛
⎝

1−6 x_k²

⎛
⎝

1−x_k

⎞
⎠

⎪
⎪
⎪
⎪

N−1

−k

⎪
⎪
⎪
⎪

≤

N−1

⎛
⎝

1−x_k

⎞
⎠

³,

otherwise,

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

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

followed by scatterplot(L).