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. The boxcar function can be expressed in terms of the uniform distribution as
where f(a,b;x) is the uniform distribution of x for the interval [a, b] and is the Heaviside step function.
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.
The function is named after its graph's resemblance to a boxcar, a type of railroad car.
- ^ Weisstein, Eric W. "Boxcar Function". MathWorld. Retrieved 13 September 2013.