stylistic:style_transfer
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 (t a) = Π (t a) = { 0, if | t | > a 2 1 2, if | t | = a 2 1, if | t | < a 2. {\displaystyle \operatorname {rect} \left({\frac {t}{a}}\right)=\Pi \left({\frac {t}{a}}\right)=\left\{{\begin{array}{rl}0,&{\text{if }}|t|>{\frac {a}{2}}\\{\frac {1}{2}},&{\text{if }}|t|={\frac {a}{2}}\\1,&{\text{if }}|t|<{\frac {a}{2}}.\end{array}}\right.}

Alternative definitions of the function define rect (± 1 2) {\textstyle \operatorname {rect} \left(\pm {\frac {1}{2}}\right)} to be 0, 1, or undefined.

Its periodic version is called a rectangular wave.