Boxcar function

A graphical representation of a boxcar function.

In mathematics, a boxcar function is any function which is zero over the entire real line except for a single interval where it is equal to a constant, A; it is a simple step function. The boxcar function can be expressed in terms of the uniform distribution as

$\operatorname{boxcar}(x)= (b-a)A\,f(a,b;x),$

where f(a,b;x) is the uniform distribution of x for the interval [a, b]. As with most such discontinuous functions, there is a question of the value at the transition points. These values are probably best chosen for each individual application.

When a boxcar function is selected as the impulse response of a filter, the result is a moving average filter.

See also

• Rectangular function
• Step function