In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern 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
Uniform distribution may refer to:
* Continuous uniform distribution
* Discrete uniform distribution
* Uniform distribution (ecology)
* Equidistributed sequence
See also
*
* Homogeneous distribution
In mathematics, a homogeneous distribution ...
as
where is the uniform distribution of ''x'' for the interval and
is the
Heaviside step function
The Heaviside step function, or the unit step function, usually denoted by or (but sometimes , or ), is a step function, named after Oliver Heaviside (1850–1925), the value of which is zero for negative arguments and one for positive argum ...
.
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 boxcar is the North American (AAR) term for a railroad car that is enclosed and generally used to carry freight. The boxcar, while not the simplest freight car design, is considered one of the most versatile since it can carry most ...
, a type of
railroad car.
See also
*
Boxcar averager
A boxcar averager (alternative names are gated integrator and boxcar integrator) is an electronic test instrument that integrates the signal input voltage after a defined waiting time (trigger delay) over a specified period of time (gate width) a ...
*
Rectangular function
*
Step function
*
Top-hat filter
References
{{mathanalysis-stub
Special functions