Lesson plan
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.
Article summary
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.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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