Talk:Poisson summation formula

message: Does this help anyone understand the PSF?:
* \sum_{k \in \mathbb Z} \frac{\gamma\left(\frac {1-s} 2, (k+ \nu_0)^2 \pi x \right)}{\left( (k+\nu_0)^2 \pi \right)^\frac {1-s} 2} e^{2 \pi i (k+\nu_0) t_0}=
\sum_{k \in \mathbb Z} 
\frac {\Gamma\left(\frac s 2, \frac{(k+ t_0)^2 \pi} x \right)} {\left( (k+t_0)^2 \pi \right)^{\frac s 2}}  e^{-2 \pi i k \nu_0} .
It does nothing for me.
--Bob K (talk) 19:46, 6 May 2009 (UTC)
thread_title:  Example 

message: I had taken a bit of a wikibreak, and this article has been heavily edited since.  That is great.  But back when I was contributing to this article heavily, I made some attempt to add references, and I notice that many of the references I put in have drifted to be attached to other statements.  Has anyone been keeping up with the fact checking to make sure we are still pointing people to the correct texts?  I will do so tomorrow afternoon my time if no one else has gotten around to it.  On a stylistic note, I have some preference for harvard citations, unfortunately back in this edit  the article was moved to a mix of footnote citations and harvard citations.  Thankfully someone made the article at least self consistent. Are there any objections to me making the article consistent in the other direction?  Thenub314 (talk) 21:56, 30 June 2009 (UTC)
replies: text: A way to hedge against the kind of drift you are worried about is to be as specific as possible in the references.  I generally like to cite a Theorem number if possible, or at least a section number.  That also makes it clear which statement (or which part of the statement) the reference is intended to support.  This is just advice: I don't universally practice what I preach in this regard.  Best, Sławomir Biały (talk) 22:13, 3 July 2009 (UTC)
thread_title: References

message: None of the following examples seem especially helpful to me.  The first two and last have absolutely no context, and don't even seem worth attempting to understand.  The "Translation" property is quite obvious (see above thread), and doesn't add much to the article when it is just dumped in somewhere.  Sławomir Biały (talk) 03:12, 4 July 2009 (UTC)
thread_title:  Examples 

message: The Poisson summation formula tells me how I come from the continuous Fourier transform to a Fourier series, namely by periodic summation in time.
Now I can also get from the Fourier series to the discrete Fourier transform by periodic summation of the Fourier series:
If I sum to a period of n Fourier coefficients then this corresponds to a discrete Fourier transform of the periodic function sampled at n equally spaced points.
What is the name of this relation? HenningThielemann (talk) 19:14, 16 October 2010 (UTC)
replies: text: You might want to take this to the USENET newsgroup comp.dsp.  I would say that the DFT fundamentally is a bijective mapping of a discrete and periodic sequence of infinite length and period N, to another of the same period.  You "get there" by sampling a continuous periodic function that is bandlimited.  Being periodic, it is described by a Fourier Series, and being bandlimited, only a finite set of coefficients are non-zero and contain information.  You sample it N equally-spaced samples per period, and N samples suffice to describe it in one domain when N coefficients suffice to describe it in the other domain.  Now why this works is because of the sampling theorem which is another way to look at the Poisson summation formula.  I would say that the Poisson summation formula is the most fundamental mathematical justification for the sampling theorem. 71.169.191.235 (talk) 22:22, 16 October 2010 (UTC)

text: Answering myself: Richard Hamming in "Digital filters" proves this relation in section 10.3 "Relation between discrete and continuous expansion" (my translation from German back to English) but does not give it a name. HenningThielemann (talk) 16:29, 1 November 2010 (UTC)
thread_title: Going from Fourier series to discrete Fourier transform

message: Recent edits have (further) obscured the conditions under which the Poisson summation formula holds, by burying these conditions in a lengthy "derivations" section.  I suggest that this content should be reorganized into a separate section of its own. Sławomir Biały (talk) 18:40, 21 September 2012 (UTC)
replies: text: Oops... sorry.  I was hoping for a better review.  I was trying out an idea from another discussion (Talk:Nyquist-Shannon_sampling_theorem#Narrow_POV):  "I think you should cover it all here; start the article off as simply as possible, and then gradually wind the complexity (and mathematics) level up towards the end.TooComplicated (talk) 14:47, 17 September 2012 (UTC)
replies: text: It's no big deal, but the article current lacks a clear statement of a theorem useful for mathematicians.  I propose that a new section break be added to the derivations section after the derivation, and possibly that a clear theorem be added there. Sławomir Biały (talk) 21:49, 23 September 2012 (UTC)
thread_title:  Recent edits  

message: Some recent, very nice, content was added to Fourier transform.  I think some of this should be incorporated here, in favor of a somewhat shorter section at Fourier transform.  Sławomir Biały (talk) 20:19, 12 December 2014 (UTC)
replies: text: doubtless, but it should not actually be removed from the article on the F.T. since people have been asking for more applications to be indicated
in that article.  The previous section was practically a stub.  — Preceding unsigned comment added by 200.55.128.88 (talk) 20:35, 12 December 2014 (UTC)
thread_title:  Merge from Fourier transform 

message: Wouldn't it be better to move the definition of the fourier transform from a footnote to the main text?  While specialists may realize that some authors put 2pi in the argument of the exponential, as is done in this article, non-mathematicians who use the article might not bother to check the footnote because they may have never been exposed to this competing convention.
:Another approach is to create separate lists for Footnotes and Citations, which makes them readily distinguishable in the text.  (Done.)  It is now more apparent that the footnote is not a citation, which should make it look more interesting.--Bob K (talk) 19:01, 10 August 2015 (UTC)
thread_title:  Conventions 

message: Why not just state the assumptions as they're used? It's confusing to say that something about s_p is implied by the dominated convergence theorem without giving any indication of why that theorem would apply. There could just be something like, "under certain conditions," and then refer them to the section below. 
Is there some reason for this idiosyncratic structure? It's especially confusing in this case, where the formula in question might not even hold. - OffUse 2601:647:C900:B6C0:49FF:B875:F863:7FBB (talk) 06:02, 10 December 2022 (UTC)
thread_title:  Stating assumptions used in the derivation section in a later "applicability" section?