Talk:Dirac comb

message: This is the same as the so-called Shah function, right? -- Pgabolde 20:23, 26 August 2005 (UTC)
replies: text: \sum \delta(t-nT) 
is the Shah function or whether it needs T=1. Anyway, I created a redirect for Shah function to here. PAR 21:27, 26 August 2005 (UTC)
replies: text:  Thanks, that's what I meant to do. -- Pgabolde 15:41, 27 August 2005 (UTC)
thread_title: Shah function

message: ... to ΔT(t) or  \Delta_T(t) \  to differentiate it from the "nascent" impulse functions in the Dirac delta function article which have the same symbol with subscript as the former symbol for the Dirac comb.  two qualitatively different functions, same symbol --- bad.  r b-j 05:44, 8 June 2006 (UTC)
replies: text:  oh, and i forgot to mention that i looked up all of the articles linked to Dirac comb and fixed any reference there so we're consistent. r b-j 05:45, 8 June 2006 (UTC)
thread_title:  i changed the symbol for the Dirac comb... 

message: Is the "scaling property" mentioned somewhere in the literature?  I don't see the point of mentioning it here or how it can be of immediate used, even if it appears to be correct.  In fact, they way it is presented now does not even mention the Dirac comb function explicitly.  A more interesting scaling property is the following:
:\Delta_{T}(t) = \sum_{k=-\infty}^{\infty} \delta(t - k T) = \sum_{k=-\infty}^{\infty} \delta(T[t/T - k]) = \frac{1}{|T|} \sum_{k=-\infty}^{\infty} \delta(t/T - k) = \frac{1}{|T|} \Delta_{1}(t/T)
which means that any Dirac comb function \Delta_{T} can be obtained by an appropriate scaling of the normalized Dirac comb function \Delta_{1}.  This property is useful since it can simplify certain derivations, and we only need to remember the Fourier transform of \Delta_{1} from which the Fourier transform of \Delta_{T} easily can be derived.  --KYN 21:02, 2 August 2006 (UTC)
replies: text: knock yourself out.  there is a mention of this scaling at Dirac_delta_function#Delta_function_of_more_complicated_arguments. r b-j 20:59, 2 August 2006 (UTC)
thread_title:  Scaling property 

message: Should the article say something about what Bracewell calls the "bed of nails" function?  This and its natural higher-dimensional analogs are very important in crystallography.  It's surprising that, as far as I can tell, Wikipedia lacks an article on them.  Sławomir Biały (talk) 14:41, 4 July 2009 (UTC)
thread_title:  Bed of nails? 

message: It can be shown that 
:\delta(\sin x)=\sum_{n=-\infty}^{\infty} \delta(t - n \pi),
in case if someone is interested... Zitterbewegung Talk  23:42, 28 October 2009 (UTC)
replies: text: This seems to beg the question a bit, depending on what one means by the composition of δ with a smooth function.  This identity is a trivial consequence of the usual definition (see Dirac delta function) although it is possible that there are other ways of defining the composition in which the statement becomes more interesting (I don't know). Sławomir Biały (talk) 17:06, 21 November 2009 (UTC)
thread_title:  A fact 

message: I have to fully agree with the IP who deleted the Scaling property section.  It was contributed long ago with one of many edits by an editor who often thinks he's making the article better and isn't.  Undoing his "improvements" over the project's scope would be a full-time job.  The equation could make sense, but as it was, is just incorrect.  One quick look at the period of the the periodic function on the two sides of the equation would immediately reveal the error. 71.169.185.162 (talk) 03:59, 27 December 2011 (UTC)
replies: text: I restored the scaling property, expressed properly, with justification. PAR (talk) 04:33, 27 December 2011 (UTC)
thread_title:  Deletion of Scaling property section. 

message: Now this needs source or proof. Is it really a Schwartz distribution?  — Preceding unsigned comment added by 92.52.10.154 (talk) 12:17, 26 December 2014 (UTC)
replies: text: Added "citation needed" tag. -- intgr [talk] 13:07, 26 December 2014 (UTC)
thread_title:  Schwartz distribution? 

message: The very first equation already introduces \delta, t and T defining only T. \delta and t should be defined as well. t, by implication is time of course, and \delta one presumes is the Dirac delta function, but this is not a page in the middle of text on signal processing, rather a standalone page that should, in manner of such pages introduce terms as needed, not assume understanding.
Of course I know the challenge is always where to draw the line and some level of assumed knowledge is inescapable (we're not going to define \Sigma or k in this context for example). But \delta and t here are not in that category, IMO.
--Bwechner (talk) 04:11, 20 September 2016 (UTC)
thread_title:  Terms need defining 

message: I am puzzled by the absence of any mention that the Fourier series of the Dirac comb can be expressed purely as a sum of cosine terms. This belongs in the article. 2601:200:C000:1A0:60BA:5A24:E2E8:77BF (talk) 03:33, 7 July 2022 (UTC)
thread_title:  Shouldn't we inform readers that the imaginary terms cancel out?