Talk:Analytic signal/Archive 1

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I keep wanting to say analytic transform. Is that improper or does it not matter? - Omegatron 02:59, Sep 19, 2004 (UTC)

I suppose it's fine to say analytic transform, but my feeling is that most people will look up analytic signal, as it seems to be a more common expression (but maybe only in physics/engineering). -- Pgabolde 15:26, 19 Sep 2004 (UTC)

It should be just as proper as Hilbert transform. But note that the descriptions of Hilbert transform are usually careful to emphasize that it produces a function of the same independent variable as the input (unlike a Fourier transform, for instance). Another term that's used is analytic representation. I like that one. --Bob K 04:48, 28 November 2005 (UTC)

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This section was previously a comment in the article. — Omegatron 14:59, 1 December 2005 (UTC)

This section appears to be in need of work. The rationale for that conclusion is the final paragraph, which is embedded within the section in order to utilize $...$.

Recent changes

I added a brief description of why the analytic signal/representation is interesting to define, in the intro before the examples. It seems adequate to let the reader understand early that the concept is not defined just for fun but has some practical applictions. There is also a clear defintion which states that "analytic signal" = "analytic representation" so that a reader unfamiliar with these concepts understands that they mean the same thing. I have also stated clearly already in the intro that the concept is applied only to real-valued signals so that this restriction doesn't have to be repeated.

The text before Example 3 is expanded to make it clear why we don't apply the analytic representation to complex-valued signals.

I changed "Polar coordinates" to "Applications" to make it easier for the reader to find where some applications of the analytic representation are described.

I removed the sentence "Phase-modulated signals are sometimes referred to as constant envelope modulation". This is most likely a correct statement, but I don't see why it should be mentioned in this article. If someone believe that is an important piece of information, it should rather be inserted in the phase modulation article.

--KYN 21:35, 3 January 2006 (UTC)

Revert on March 23, 2006

The relation between analytic signal and causality in the Fourier domain was previously mentioned in this artcile, but is now moved to the causal filter article. Anyway, it should not be mentioned in the introduction to the analytic signal article. The introduction of the analytic signal should be based on its properties in the signal domain, and the relation to causality in the Fourier domain is rather a characterization of causal filter than of the analytic signal itself --KYN 11:27, 23 March 2006 (UTC)

Analytic signal and analytic continuation

Since analytic signal is used to obtain complex representation of a real signal, and analytic continuation can do the same, isn't there any connection between them? At least for harmonic signals they are the same. Is there any proof or counter-example? --Ring0 05:20, 2 May 2006 (UTC)

The change from \equiv to "="

I've copied the following question my talk page, posted by r b-j on my talk page:

Paul, can you explain the change from \equiv to = in Analytic signal?

this diff [1]

the two mathematical statements that you changed are true only because of their definition. there is no other reason for equality there other than equivalence. (you can answer here or the article talk page, i'm watching both.) r b-j 22:27, 30 October 2006 (UTC)

Hi r b-j. Because of its inherent ambiguity, the symbol "≡" should be avoided (where possible). See the discussion at: Wikipedia talk:WikiProject Mathematics#Convention for definitions: Use := or \equiv?. I felt that simply replacing "≡" by an equal sign would be sufficient here. But perhaps some rewording would be better? Paul August ☎ 17:02, 31 October 2006 (UTC)

links to this article don't work (today)

This link does not work:

http://en.wikipedia.org/w/index.php?title=Analytic_signal

But this one does:

http://en.wikipedia.org/w/index.php?title=Analytic_signal&oldid=144144803

--Bob K 13:13, 5 September 2007 (UTC)

Now it works.

--Bob K 12:55, 6 September 2007 (UTC)