# What's it called: single square wave mathematical function

**URL:** <https://boards.straightdope.com/t/whats-it-called-single-square-wave-mathematical-function/173991>\
**Category:** Factual Questions\
**Created:** [May 8, 2003, 10:51pm UTC](https://boards.straightdope.com/t/whats-it-called-single-square-wave-mathematical-function/173991 "2003-05-08T22:51:05Z")\
**Posts on this page:** 12\
**Page:** 1

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**Author:** ![Napier](https://avatars.discourse-cdn.com/v4/letter/n/ce73a5/32.png) [@Napier](https://boards.straightdope.com/u/Napier)\
**Post date:** [May 8, 2003, 10:51pm UTC](https://boards.straightdope.com/t/whats-it-called-single-square-wave-mathematical-function/173991/1 "2003-05-08T22:51:05Z")

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What’s the name of the mathematical function whose value is zero almost everywhere but 1 or some constant value in a finite region, maybe:  
y = 1 if -1 \< x \< +1, else y = 0  
or at least anything that is a single rectangular pulse?  
We were thinking “Heaviside”, but that’s a step that is 1 for all x\>0, it never goes back down.

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**Author:** ![Jabba](https://avatars.discourse-cdn.com/v4/letter/j/b5e925/32.png) [@Jabba](https://boards.straightdope.com/u/Jabba)\
**Post date:** [May 8, 2003, 10:56pm UTC](https://boards.straightdope.com/t/whats-it-called-single-square-wave-mathematical-function/173991/2 "2003-05-08T22:56:58Z")

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The function you describe is the indicator function of the interval (-1,1). Indicator functions are special cases of step functions.

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**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\
**Post date:** [May 8, 2003, 11:10pm UTC](https://boards.straightdope.com/t/whats-it-called-single-square-wave-mathematical-function/173991/3 "2003-05-08T23:10:23Z")

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They’re also commonly known as characteristic functions. Given a subset E of some given domain, the characteristic function of E is defined to be 1 at points in E, and 0 elsewhere.

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**Author:** ![Jabba](https://avatars.discourse-cdn.com/v4/letter/j/b5e925/32.png) [@Jabba](https://boards.straightdope.com/u/Jabba)\
**Post date:** [May 8, 2003, 11:12pm UTC](https://boards.straightdope.com/t/whats-it-called-single-square-wave-mathematical-function/173991/4 "2003-05-08T23:12:59Z")

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Characteristic! That’s the word I meant. Indicator is for random variables, sorry.

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**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\
**Post date:** [May 9, 2003, 12:20am UTC](https://boards.straightdope.com/t/whats-it-called-single-square-wave-mathematical-function/173991/5 "2003-05-09T00:20:23Z")

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Well, you can get that function by multiplying Heaviside functions. Consider f(x) = H(x - 1)H(1 - x). It’s equal to one for -1 \< x \< 1 and 0 elsewhere.

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**Author:** ![Omphaloskeptic](https://avatars.discourse-cdn.com/v4/letter/o/bcef8e/32.png) [@Omphaloskeptic](https://boards.straightdope.com/u/Omphaloskeptic)\
**Post date:** [May 9, 2003, 2:10am UTC](https://boards.straightdope.com/t/whats-it-called-single-square-wave-mathematical-function/173991/6 "2003-05-09T02:10:08Z")

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It’s also sometimes called a top-hat function, or a square pulse.

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**Author:** ![Race\_Bannon](https://avatars.discourse-cdn.com/v4/letter/r/5f8ce5/32.png) [@Race\_Bannon](https://boards.straightdope.com/u/Race_Bannon)\
**Post date:** [May 10, 2003, 3:42am UTC](https://boards.straightdope.com/t/whats-it-called-single-square-wave-mathematical-function/173991/7 "2003-05-10T03:42:57Z")

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In signal analysis, I’ve heard it called a Boxcar function, or Rectangular window.

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**Author:** ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)\
**Post date:** [May 10, 2003, 5:10am UTC](https://boards.straightdope.com/t/whats-it-called-single-square-wave-mathematical-function/173991/8 "2003-05-10T05:10:58Z")

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> [@](#):
>
> \*Originally posted by ultrafilter \*  
> \*\*Well, you can get that function by multiplying Heaviside functions. Consider f(x) = H(x - 1)H(1 - x). It’s equal to one for -1 \< x \< 1 and 0 elsewhere. \*\*

Or f(x) = H(x + 1) - H(x - 1).

I don’t think there’s anything wrong with the term “rectangular pulse function”.

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**Author:** ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)\
**Post date:** [May 10, 2003, 5:52am UTC](https://boards.straightdope.com/t/whats-it-called-single-square-wave-mathematical-function/173991/9 "2003-05-10T05:52:46Z")

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Or even “inverse sinc function”.

H(x + 1) - H(x - 1) = L[sup]-1[/sup]{sin(ω/2)/(ω/2)}

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**Author:** ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)\
**Post date:** [May 10, 2003, 6:03am UTC](https://boards.straightdope.com/t/whats-it-called-single-square-wave-mathematical-function/173991/10 "2003-05-10T06:03:37Z")

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Or even “inverse sinc function”.

H(x + 1) - H(x - 1) = L[sup]-1[/sup]{sin(ω/2)/(ω/2)}

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**Author:** ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)\
**Post date:** [May 10, 2003, 6:25am UTC](https://boards.straightdope.com/t/whats-it-called-single-square-wave-mathematical-function/173991/11 "2003-05-10T06:25:59Z")

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On second thought, “inverse sinc function” is too ambiguous to be very useful.

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**Author:** ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)\
**Post date:** [May 10, 2003, 6:50am UTC](https://boards.straightdope.com/t/whats-it-called-single-square-wave-mathematical-function/173991/12 "2003-05-10T06:50:36Z")

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On second thought, “inverse sinc function” is too ambiguous to be very useful.