Dictionary:Boxcar

A rectangular window function:

$box_{a}(t)={\begin{Bmatrix}0,&t<-a/2\\1,&-a/2<t<a/2\\0,&t>a/2\end{Bmatrix}}$.

Its transform is

$box_{a}(t)\leftrightarrow a\;sinc\left({\frac {\pi a}{t}}\right)=a\;{\frac {sin({\frac {\pi a}{t}})}{\frac {a\pi }{t}}}$.

Sometimes called a gate.

External links

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