Blackman-Harris window function : blackman_harris

5.27.13 Blackman-Harris window function : blackman_harris_window

blackman_harris_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=a₀−a₁ cos

⎛
⎜
⎜
⎝

2 k π

N−1

⎞
⎟
⎟
⎠

+a₂ cos

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⎜
⎜
⎝

4 k π

N−1

⎞
⎟
⎟
⎠

−a₃ cos

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⎜
⎜
⎝

6 k π

N−1

⎞
⎟
⎟
⎠

for k=0,1,…,N−1 , where a₀=0.35875 , a₁=0.48829 , a₂=0.14128 and a₃=0.01168 . For example, input :

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

followed by scatterplot(L).