Inmathematics, aboxcar function is anyfunction which is zero over the entirereal line except for a singleinterval where it is equal to a constant,A.[1] The function is named after its graph's resemblance to aboxcar, a type ofrailroad car. The boxcar function can be expressed in terms of theuniform distribution aswheref(a,b;x) is the uniform distribution ofx for the interval[a,b] and is theHeaviside step function. As with most suchdiscontinuous functions, there is a question of the value at the transition points, which are usually best chosen depending on the individual application.
When a boxcar function is selected as theimpulse response of afilter, the result is asimple moving average filter, whosefrequency response is asinc-in-frequency, a type oflow-pass filter.
 | Thismathematical analysis–related article is astub. You can help Wikipedia byadding missing information. |