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5.23.20  Tukey window function : tukey_window

tukey_window takes as arguments a real vector v of length n and optionally a real number α∈[0,1] (by default α=0.5 ) and/or 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=n2n1+1 defined by

wk=












1
2
 


1+cos


π 


k
β
−1








,
k<β,
1,
β≤ k≤(N−1) 


1−
α
2



,
1
2
 


1+cos


π 


k
β
2
α
+1








,
otherwise,

where β=α (N−1)/2 , for k=0,1,…,N−1 . When α=0 the rectangular window function (on-off windowing) is obtained, and the case α=1 corresponds to the Hann window function. For example, input :

L:=tukey_window(randvector(1000,0..1),0.4):;

followed by scatterplot(L).


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