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.

[1] The function is named after its graph's resemblance to a boxcar, a type of railroad car.

The boxcar function can be expressed in terms of the uniform distribution as

As with most such discontinuous functions, there is a question of the value at the transition points.

When a boxcar function is selected as the impulse response of a filter, the result is a simple moving average filter, whose frequency response is a sinc-in-frequency, a type of low-pass filter.