Rectangular function

The rectangular function, also rect function, is a discontinuous mathematical function with the following definition:

Alternative definitions, which are common, especially in the field of signal processing, the rectangular function put something deviating firm as:

The rectangular function can also be expressed with the help of the Heaviside function as:

The Fourier transform of the square function, the sinc function results:

Shifting and scaling

A rectangular function centered on and has a duration of, is expressed by

Derivation

The rectangular function is differentiable as a discontinuous function neither in the classical sense, nor is it weakly differentiable. However, a distribution derivative is the Dirac delta function δ possible:

Other correlations

The convolution of two identical rectangular functions yields the delta function, the integration of a ramp function. A form with periodic continuation of the rectangle are the Rademacher function.

The multiple convolution with folds

Results for with an appropriate scaling the Gaussian bell curve.