Talk:Dirac delta function

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Good articleDirac delta function has been listed as one of the Mathematics good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it.
Article milestones
DateProcessResult
September 29, 2010Good article nomineeNot listed
October 1, 2010Good article nomineeListed
Current status: Good article


Unit impulse symbol?[edit]

In this early 2012 edit we got that it's called the "unit impulse symbol" in signal processing, according to Bracewell's 1986 book in which Chapter 5 is titled "The impulse symbol". I don't have the book handy to see how he uses the term, but I suspect in reference to the Greek delta symbol itself, similar to how he does for the 2D delta in this 2012 book. Or perhaps he's just trying to make sure he doesn't call it a function. But in signal processing it's pretty much always called the "unit impulse function", or just "unit impulse". See book n-gram stats (note that "unit impulse symbol" is not common enough in books to appear in the stats). Sadly, however, now we have "unit impulse symbol" showing up for this in books starting in 2013; see book search.

@Slawekb: If you or someone has Bracewell's 1986 book handy, please tell us exactly what it says; in the meantime, I'm going to try to "fix" this per other refs. Dicklyon (talk) 18:01, 31 May 2022 (UTC)[reply]

Misleading implication that bell curves are bump functions[edit]

From the introduction: "[...] or as the weak limit of a sequence of bump functions (e.g., ) [...]".

But the given example is not a collection of bump functions (they are supported on all of ), so this is misleading. 83.91.88.220 (talk) 09:59, 22 February 2023 (UTC)[reply]

Does this abuse of notation used in the text an accurate treatment[edit]

In the section "Resolutions of the identity" (https://en.wikipedia.org/wiki/Dirac_delta_function#Resolutions_of_the_identity) it is said: "Nevertheless, it is common to abuse notation and write:

"

when the accurate result is:

with the Heaviside step function and it is the integration constant.

I don't have a clue about what it is the topic about, but it could be nice to include the explanation about why in the specific used described both formulations could be used equivalently. 191.125.179.92 (talk) 19:57, 22 March 2023 (UTC)[reply]

It is an abuse of notation not for the reason you state, but because this is not an integral of a function. 74.111.98.156 (talk) 12:56, 4 July 2023 (UTC)[reply]

Proposal: change name from Dirac delta function to Dirac delta distribution[edit]

I suggest to rename the mathematical object and the page "Dirac delta distribution". Although using the word function is common, it is also common to call it distribution, which is more appropriate mathematically. Skater00 (talk) 16:35, 21 March 2024 (UTC)[reply]

I think WP:COMMONNAME favors the current "Dirac delta function". I will add another reason for keeping things as they are: prospective readers of the article will all have heard of "function", but not know "distribution", and may as a result be uncertain whether they have arrived at the correct article. Thus the current naming is the least likely to cause confusion. Tito Omburo (talk) 09:10, 22 March 2024 (UTC)[reply]