Pravougaona funkcija Pravougaona funkcija [ 1] funkcija pravougaonika i jedinični impuls ) je funkcija definisana kao:
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{\displaystyle \mathrm {rect} (t)=\sqcap (t)={\begin{cases}0&{\mbox{if }}|t|>{\frac {1}{2}}\\[3pt]{\frac {1}{2}}&{\mbox{if }}|t|={\frac {1}{2}}\\[3pt]1&{\mbox{if }}|t|<{\frac {1}{2}}.\end{cases}}}
Alternativna definicija funkcije kaže da
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{\displaystyle \mathrm {rect} (\pm {\begin{matrix}{\frac {1}{2}}\end{matrix}})}
Heavisideove odskočne funkcije ,
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{\displaystyle u(t)}
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{\displaystyle \mathrm {rect} \left({\frac {t}{\tau }}\right)=u\left(t+{\frac {\tau }{2}}\right)-u\left(t-{\frac {\tau }{2}}\right),\,}
ili, na drugi način:
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{\displaystyle \mathrm {rect} (t)=u\left(t+{\frac {1}{2}}\right)\cdot u\left({\frac {1}{2}}-t\right).\,}
Jedinične Fourierove transformacije pravougaone funkcije su:
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{\displaystyle \int _{-\infty }^{\infty }\mathrm {rect} (t)\cdot e^{-i2\pi ft}\,dt={\frac {\sin(\pi f)}{\pi f}}=\mathrm {sinc} (f),\,}
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{\displaystyle {\frac {1}{\sqrt {2\pi }}}\int _{-\infty }^{\infty }\mathrm {rect} (t)\cdot e^{-i\omega t}\,dt={\frac {1}{\sqrt {2\pi }}}\cdot \mathrm {sinc} \left({\frac {\omega }{2\pi }}\right),\,}
gdje je
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{\displaystyle \mathrm {sinc} }
Možemo definisati trougaonu funkciju kao konvoluciju dvije pravougaone funkcije:
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{\displaystyle \mathrm {tri} (t)=\mathrm {rect} (t)*\mathrm {rect} (t).\,}
![{\displaystyle \mathrm {rect} (t)=\sqcap (t)={\begin{cases}0&{\mbox{if }}|t|>{\frac {1}{2}}\\[3pt]{\frac {1}{2}}&{\mbox{if }}|t|={\frac {1}{2}}\\[3pt]1&{\mbox{if }}|t|<{\frac {1}{2}}.\end{cases}}}](/media/api/rest_v1/media/math/render/svg/f245b8e1ae2b29983b6d85b3d3338ef53f1bae07)
