Rectangular function

The rectangular function (also known as the rectangle function, rect function, Pi function, gate function, unit pulse, or the normalized boxcar function) is defined as Alternative definitions of the function define rect ⁡ ( ± 1 2 ) {displaystyle operatorname {rect} left(pm {frac {1}{2}} ight)} to be 0, 1, or undefined. The rectangular function is a special case of the more general boxcar function: where u {displaystyle u} is the Heaviside function; the function is centered at X {displaystyle X} and has duration Y {displaystyle Y} , from X − Y / 2 {displaystyle X-Y/2} to X + Y / 2 {displaystyle X+Y/2} . The unitary Fourier transforms of the rectangular function are using ordinary frequency f, and using angular frequency ω, where s i n c {displaystyle mathrm {sinc} } is the unnormalized form of the sinc function.