### 5.23.12 Gaussian window function : gaussian_window

gaussian_window takes as arguments a real vector v of length n and optionally a positive real number α≤ 0.5 (by default α=0.1 ) and/or an interval n_{1} .. n_{2} (with default values n_{1}=0 and n_{2}=n−1 ), and returns the elementwise product of the vector [v_{n1},…,v_{n2}] and the vector w of length N=n_{2}−n_{1}+1 defined by

w_{k}=exp | ⎛
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for k=0,1,…,N−1 . For example, input :

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

followed by scatterplot(L).