Talk:Dirac delta function

Article review

It has been a while since this has been reviewed, so I took a look and noticed the following:

• The GA review consisted of a checkmark, and did not include any details on what checks were conducted. While today's extensive reviews might not have been necessary back then, I think a little bit more information was still necessary. Other reviewers might want to spotcheck the article against the criteria.
• There is a lot of uncited text. Some uncited statements are covered under WP:CALC. Other statements such as the following do need citations (and I can add other "citation needed" templates if requested:

• "The Dirac delta is used to model a tall narrow spike function (an impulse), and other similar abstractions such as a point charge, point mass or electron point"
• "In applied mathematics, as we have done here, the delta function is often manipulated as a kind of limit (a weak limit) of a sequence of functions, each member of which has a tall spike at the origin"
• "In probability theory and statistics, the Dirac delta function is often used to represent a discrete distribution, or a partially discrete, partially continuous distribution, using a probability density function (which is normally used to represent absolutely continuous distributions)." do need citations to verify this information.

• There is POV and opinionated language in the article, such as "Unfortunately, the actual limit of the functions (in the sense of pointwise convergence) is zero everywhere" (Why is this unfortunate?) and "Although using the Fourier transform, it is easy to see that this generates a semigroup in some sense" (it may not be easy for the reader to see). These were found in a quick skim: I think the entire article might need a copyedit to ensure that POV languauge is removed.

Should this article go to WP:GAR? Z1720 (talk) 01:14, 29 June 2025 (UTC)

@Z1720 Sorry but can you please wait until Matrix (mathematics) and Addition are completely improved? Some users may not have the time to improve it. Dedhert.Jr (talk) 11:04, 29 June 2025 (UTC)

• @Dedhert.Jr: Happy to wait! If editors offer to improve an article, I won't send it to GAR. Z1720 (talk) 14:12, 29 June 2025 (UTC)

If you want to tag some things, I'm happy to work on it if I have the time. Tito Omburo (talk) 18:04, 29 June 2025 (UTC)

@Tito Omburo: I added some citation needed tags per the request above. I probably did not get them all, so if you find a citation to put somewhere, I recommend it. Z1720 (talk) 18:22, 29 June 2025 (UTC)

Thanks! Tito Omburo (talk) 21:10, 29 June 2025 (UTC)

We've added significantly better citations. The article may need other cleanup that we haven't looked at. Tito Omburo (talk) 20:39, 3 August 2025 (UTC)

Picture

Motivation could use a picture. A tall spike, area one, centered at 0. A parameter like "resolution", determining semiwidth and height (=1/"resolution"). Tito Omburo (talk) 20:38, 8 July 2025 (UTC)

Undefined reference

There are references to {{sfn|Stein|Shakarchi|2007}} but no such source is listed, nor, as far as I can see, has it ever been. DuncanHill (talk) 17:53, 15 February 2026 (UTC)

Increase visibility / prominence of the Fourier Transform section

This section should be emphasized more in my opinion; it’s not very easy to find and it’s quite important, in physics at least. Was surprised it’s not highlighted more, even if many of the definition/ representations of it as a function are shaky. ~2026-34339-71 (talk) 06:02, 11 June 2026 (UTC)

I agree with this. The Fourier transform is buried in the representations section, and while it does discuss the Fourier representation of delta as such, it doesn't really do much in the way of Fourier analysis. I think Fourier transform (or Fourier analysis) should probably be a separate section, which actually does something. Sławomir Biały (talk) 06:57, 11 June 2026 (UTC)