Talk:Dirac comb

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Geometry guy 15:30, 10 June 2007 (UTC)

This is the same as the so-called Shah function, right? -- Pgabolde 20:23, 26 August 2005 (UTC)

I think so - I don't know if

$\sum \delta(t-nT)$

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)

Thanks, that's what I meant to do. -- Pgabolde 15:41, 27 August 2005 (UTC)

1 i changed the symbol for the Dirac comb...
2 Scaling property
3 The shah symbol
4 Fourier transform

[edit] i changed the symbol for the Dirac comb...

... to Δ_T(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)

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)

[edit] Scaling property

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 $Δ T$ can be obtained by an appropriate scaling of the normalized Dirac comb function $Δ 1$ . This property is useful since it can simplify certain derivations, and we only need to remember the Fourier transform of $Δ 1$ from which the Fourier transform of $Δ T$ easily can be derived. --KYN 21:02, 2 August 2006 (UTC)

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)

Yes, I see it, but can you please tell me what information the "Scaling property" section of the article provides about the comb function? --KYN 21:02, 2 August 2006 (UTC)

[edit] The shah symbol

The article refers to Bracewell and he uses the shah-symbol $I I I (t)$ to denote the Dirac comb function. If Bracewell is the base reference, why not stick to that symbol and why not call it the shah function, instead of using $Δ$ and mainly call it the Dirac comb function? In principle, it doesn't matter much to me which notation and names are used as long as they can be motivated. If we are going to use $Δ$ and Dirac comb function, I would like to see a reference which establishes this notation and name. --KYN 21:00, 2 August 2006 (UTC)

Bracewell isn't the only reference about the Dirac comb. Oppenheim and Schafer is an authorative reference and they call it s(t). your "shah" function is just three letters: "I" and what we should really get is the cyrillic symbol. r b-j 21:05, 2 August 2006 (UTC)

OK, I agree that the shah symbol may appear somewhat shaky through the pseudo-latex renderer, even though it may be possible to make the wiki-guys to implement a proper shah symbol. Why not stick to s(t) and add Oppenheim and Schafer to the reference list? Where does the $Δ$ symbol comes from? --KYN 22:36, 2 August 2006 (UTC)

[edit] Fourier transform

Why $\quad {1\over T}\sum_{k=-\infty}^{\infty} \delta \left( f - {k\over T} \right) \quad = \sum_{n=-\infty}^{\infty} e^{-i2\pi fnT}$ ? Thank you. --Abdull 18:52, 12 June 2007 (UTC)