矩形函数

$ \sqcap:\Complex\ni t\mapsto\frac12\llbracket|t|=\frac12\rrbracket+\llbracket|t|<\frac12\rrbracket\in\Bbb Q

性質

$ \sqcap(t)=u\left(t+\frac12\right)u\left(\frac12-t\right)

$ =\frac12\left(\operatorname{sgn}\left(t+\frac12\right)+1\right)\frac12\left(\operatorname{sgn}\left(\frac12-t\right)+1\right)

$ \mathcal F(\sqcap)(\omega)=\frac1{\sqrt{2\pi}}\operatorname{sinc}\left(\frac\omega2\right)