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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*.^{[1]} 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.