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 . 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 : \operatorname{boxcar}(x)= (b-a)A\,f(a,b;x) = A(H(x-a) - H(x-b)), where f(a,b;x) is the uniform distribution of x for the interval [a,b] and H(x) is the Heaviside step function. As with most such discontinuous 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 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.

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 . 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 \operatorname{boxcar}(x)= (b-a)A\,f(a,b;x) = A(H(x-a) - H(x-b)), where f(a,b;x) is the uniform distribution of x for the interval [a,b] and H(x) is the Heaviside step function. As with most such discontinuous 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 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==

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