Talk:Fourier transform

message: I was hoping to see an IPA pronunciation in the first sentence of the article (but there is not one). Wiktionary has an English pronunciation for Fourier (as a surname), which might apply to Fourier transform. - excarnateSojourner (talk|contrib) 21:30, 11 July 2022 (UTC)
replies: text: In English the name is often pronounced foo-ree-ei or foor-ee-ei (the last syllable rhyming with "day", and all three syllables given approximately equal stress). 2601:200:C000:1A0:BC00:5039:DB55:E9EC (talk) 22:23, 29 July 2022 (UTC)
thread_title:  Pronunciation 

message: The section idiotically titled Introduction contains this passage:
"Although Fourier series can represent periodic waveforms as the sum of harmonically-related sinusoids, Fourier series can't represent non-periodic waveforms. However, the Fourier transform is able to represent non-periodic waveforms as well. It achieves this by applying a limiting process to lengthen the period of any waveform to infinity and then treating that as a periodic waveform.."
The last sentence is complete mathematical nonsense, and is not taken from the cited reference. 2601:200:C000:1A0:BC00:5039:DB55:E9EC (talk) 19:13, 29 July 2022 (UTC)
thread_title:  Nonsense statement 

message: As I tried to write a few clarifying sentences in the section Fourier transform for functions that are zero outside an interval, in order to specify the periodic function whose Fourier series was referred to ... I realized that the article refers to the same function when discussing the Fourier transform. But: It's not the same function. One is periodic and the other is zero outside the interval [-T/2, T/2]. 
I hope someone knowledgeable about this subject can fix this apparent problem. 2601:200:C000:1A0:BC00:5039:DB55:E9EC (talk) 20:08, 29 July 2022 (UTC)
thread_title:  Possible problem may need fixing 

message: Well done, but it repeats a lot of information available thru WikiLinks, and now also added to Fourier transform#The analysis formula.  IMO this section can be downsized or eliminated. Bob K (talk) 16:47, 12 December 2022 (UTC)
thread_title:  Section:  Use of complex sinusoids to represent real sinusoids 

message: It has been a decade since the ξ_vs_ν_? discussion between just 2 editors. And as noted then, ν was the original preference, replaced without a consensus.  Now I am asking if there is any consensus for reverting back to ν, because ξ is unnecessarily intimidating-looking (IMO).
--Bob K (talk) 00:59, 19 December 2022 (UTC)
replies: text: I am not in favor of this. This is a bit like avoiding \theta for an angle. Thenub314 (talk) 21:30, 15 February 2023 (UTC)
thread_title:  ξ vs ν ? revisited 

message: The reliance on:
: \sum_{n=-\infty}^{\infty} e^{-i \omega n T} = \frac{2 \pi}{T} \sum_{k=-\infty}^{\infty} \delta(\omega-2\pi k/T)
is no better than relying on the transform pair:
:e^{ i 2\pi \xi_0 x}\ \stackrel{\mathcal{F}}{\longleftrightarrow}\ \delta \left(\xi - \xi_0\right).
Consequently, you've made a mountain out of a molehill.
--Bob K (talk) 01:59, 25 December 2022 (UTC)
thread_title:  Section:  Fourier transform for periodic functions 

message: The result of this section seems to be the statement:
Under appropriate conditions, the Fourier series of  will equal the function . In other words,  can be written:
:f(x)=\sum_{n=-\infty}^\infty c_n\, e^{2\pi i\left(\frac{n}{T}\right) x} =\sum_{n=-\infty}^\infty \hat{f}(\xi_n)\ e^{2\pi i\xi_n x}\Delta\xi,
At the very least it needs to clarified that the first equality only applies in the interval T.
But also we already know that f(x) can be recovered from \hat f(\xi).  So what you are showing is that when its domain is bounded, it can also be recovered from discrete samples of \hat f(\xi), which, by the way, is the dual of the time domain sampling theorem.  This is mildly interesting, but it strikes me as a proof looking for a home, and the whole article is already pretty cluttered with stuff.
--Bob K (talk) 09:00, 27 December 2022 (UTC)
thread_title:  Section:  Fourier transform for functions that are zero outside an interval 

message: I removed a reference from here because the cited reference wasn't discussing the Fourier transform in the section indicated.  I will try to find something more specific to this topic. Thenub314 (talk) 20:47, 16 February 2023 (UTC)
thread_title:  Symmetry section 

message: The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion:
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Participate in the deletion discussion at the . —Community Tech bot (talk) 14:53, 17 February 2023 (UTC)
thread_title:  A Commons file used on this page or its Wikidata item has been nominated for deletion 

message: In the inversion section the integrals are over the variable σ but the variable ξ appears in the integrands.  Where does the ξ come from?  — Preceding unsigned comment added by 2.27.171.228 (talk) 21:25, 21 August 2023 (UTC)
thread_title:  Error in inversion section?