Talk:Wigner distribution function

Module:WikiProject banner/doc
This page is a soft redirect.

Statistics Start‑class Low‑importance

	This article is within the scope of WikiProject Statistics, a collaborative effort to improve the coverage of statistics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.StatisticsWikipedia:WikiProject StatisticsTemplate:WikiProject StatisticsStatistics
Start	This article has been rated as Start-class on Wikipedia's content assessment scale.
Low	This article has been rated as Low-importance on the importance scale.

Mathematics Start‑class Low‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics
Start	This article has been rated as Start-class on Wikipedia's content assessment scale.
Low	This article has been rated as Low-priority on the project's priority scale.

example

I just changed the caption of the image so that it does not advertises an unknown method. SinPantuflas (talk) 09:39, 7 November 2017 (UTC)[reply]

autocorrelation

If it is indeed an autocorrelation that is meant, then it is not a time-reversed copy. Auto correlation uses the cross-correlation (shifted), not the convolution (time-reversed, shifted). The current article text essentially suggests one operation, but explains the other. I am not so experienced with integral transforms, but it appears to indeed be a time-reversed, shifted copy based on the definition given. That means that is more like an autoconvolution. This term exists, but doesn't have a Wikipedia page. Any other mathematicians care to weigh in?--75.80.43.80 (talk) 23:39, 18 April 2011 (UTC)[reply]

I do not see how it can be that "The WDF is essentially the Fourier transform of the input signal’s autocorrelation function". The link to autocorrelation shows that the autocorrelaiton itself is an integral. None of it appears in the definition of the WDF. What about removing this sentence? — Preceding unsigned comment added by 130.246.132.178 (talk) 14:34, 12 September 2013 (UTC)[reply]

I fixed this part of the article. Lots of stuff could be added to this article, like references to Ville and sections on negativity and the uncertainty principle. But I don't agree with merging this with the QM article, because the wave function and a time series are two very different things with very different interpretations... even though there will necessarily be many redundant/analogous relations. CHF (talk) 18:45, 19 September 2013 (UTC)[reply]

Time-Frequency Resolution

The article claims "the Wigner distribution function provides the highest possible temporal vs frequency resolution which is mathematically possible within the limitations of uncertainty in quantum wave theory. " without giving a source. I do not understand how a mathematical operation can be bound by some physical theory. I doubt this claim. I guess there is some lower bound one can show for a class of transformations which is achieved by the wigner distribution function and that this bound also occurs somewhere in the quantum wave theory. — Preceding unsigned comment added by 2A01:C22:8842:E400:15C:A911:1061:A3B3 (talk) 16:53, 25 April 2020 (UTC)[reply]

I suspect your are misreading the admittedly loose statement. There is no physics involved, and the allusion to "quantum wave theory" is just shorthand for the uncertainty principle, a property of Fourier analysis, so pure math. It' just that most readers recognize the inequality as a quantum mechanical principle. Mere language. Cuzkatzimhut (talk) 17:59, 25 April 2020 (UTC)[reply]

Perhaps you could quantify this idea (or point to a source) for the mathematically challenged among us. I can intuit that the resolution of the spectral content vs. time for the Wigner Transform would be much better than say the straightforward Short Time Fourier Transform method but could you help quantify that? Sdwehe (talk) 15:27, 28 July 2022 (UTC)[reply]