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.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> 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 <math display="block">\operatorname{boxcar}(x)= (b-a)A\,f(a,b;x) = A(H(x-a) - H(x-b)),</math> where Template:Math is the uniform distribution of x for the interval Template:Closed-closed and <math>H(x)</math> 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 simple moving average filter, whose frequency response is a sinc-in-frequency, a type of low-pass filter.