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Rectangular function

The rectangular function (also known as the rectangle function, rect function, Pi function, Heaviside Pi function, gate function, unit pulse, or the normalized boxcar function) is defined as rect⁡(tT)=Π(tT)={0,if |t|>T212,if |t|=T21,if |t|<T2.{\displaystyle \operatorname {rect} \left({\frac {t}{T}} ight)=\Pi \left({\frac {t}{T}} ight)=\left\{{\begin{array}{rl}0,&{\text{if }}|t|>{\frac {T}{2}}\\{\frac {1}{2}},&{\text{if }}|t|={\frac {T}{2}}\\1,&{\text{if }}|t|<{\frac {T}{2}}.\end{array}} ight.}Alternative definitions of the function define rect⁡(t=±T2){\textstyle \operatorname {rect} \left(t=\pm {\frac {T}{2}} ight)} to be 0, 1, or undefined.

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