Boxcar function
![](http://upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Boxcar_function.svg/250px-Boxcar_function.svg.png)
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 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 simple moving average filter, whose frequency response is a sinc-in-frequency, a type of low-pass filter.
See also
- Boxcar averager
- Rectangular function
- Step function
- Top-hat filter
References
- ^ Weisstein, Eric W. "Boxcar Function". MathWorld. Retrieved 13 September 2013.
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