The rectangular function (also known as the rectangle function or the normalized boxcar function) is defined as

or in terms of the Heaviside step function

The rectangular function is normalized:

The Fourier transform of the rectangular function is

where "sinc" is the sinc function. Viewing the rectangular function as a probability distribution function, its characteristic function is therefore written

and its moment generating function is:

where "sinh" is the hyperbolic sine function.

See also

• Fourier transform
• square wave