Talk:Instantaneous phase

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KYN says "Please be more specific about what's wrong with the application section rather than removing it."

It either needs more detail or it needs to go out, because neither of the articles it references, image processing and computer vision, corroborate the claim that is made.

More details perhaps, but I don't understand the argument that this article needs to be corroborated by the computer vision or image processing articles to stay. These articles provide overviews of larger application areas and do not mention specific techniques for solving problems. Please refer to the books by Cohen or Granlund & Knutsson for more substantial support.
Sorry, I did not realize those references corroborate the article content. But I will happily take your word for it.
--Bob K 22:30, 27 June 2007 (UTC)

Also, if it stays, someone needs to make the change I already indicated; i.e., the maxima occur at \phi(t) = {\pi \over 2} + N\cdot 2 \pi,  and the minima occur at \phi(t) = -{\pi \over 2} + N\cdot 2 \pi,  for integer values of N.  And the points of maximum slope are the multiples of \pi.\,  But why are we reiterating this mundane detail about sin() functions here? Easier and better to link them to sinusoid, where they can see for themselves on a graph.

This confusion was introduced by you own edits on 2006-06-28T01:55:27. Prior to that, there was no explicit reference to a sin function. The instantaneous phase is defined as the argument of the analytic signal, and it does equal 0 at the local maxima of either a sin and a cos function!!
I see what you mean. I had actually forgotten that bit of history.
But I still don't agree with the part of your comment that I emboldened. sin(0)=0.
--Bob K 22:30, 27 June 2007 (UTC)
A reference to the sinusoid article is OK, BUT one of the main points of the instantaneous phase is that, because it is defined from the analytic representation, it is well-defined for (almost) any signal (at least when the corresponding analytic signal is non-zero).

--Bob K 18:00, 27 June 2007 (UTC)

I would like to revert to the 2006-03-27T08:53:15 version. It provides the following information:

  • The formal definition in the first paragraph (The current version suggests that the instantaneous phase must be related to a sin function. This is not correct)
  • A discussion on the representation since the argument function of a complex function can be represented in different ways (this is relevant for various applications which use the instantaneous phase in practice)
  • A summary of the motivation for using phase in computer vision (here one could add a reference to instantaneous frequency, which is derived from the instantaneous phase).

Yes/No? --KYN 20:46, 27 June 2007 (UTC)

Wikipedia is killing me right now. I lost edits about 6 times already, just trying to "preview". Also, I'm packing for a trip and need to finish and get some sleep. So do what you think is best, and maybe we will reconnect here some time in the future. Please think about the fact that analytic signals aren't the only things with an instantaneous phase. Even the moon has one. As best I can recall, that was the original reason to trying to "generalize" to other kinds of things.
--Bob K 22:38, 27 June 2007 (UTC)

In order to solve this issue we need to agree on what instantaneous phase means. Clearly, phase has a very broad meaning which can be seen in the Phase article. However, the concept instantaneous phase has a very precise meaning related to an (in principle) arbitrary function or signal, it is the argument of the corresponding analytic signal. It offers two interesting properties which are relevant in signal processing:

  • It provides a useful definition of phase for functions/signals which are not of cos/sin-type, even though this phase value may not be meaningful in all cases.
  • This phase value is independent of the reference coordinate (e.g. time) used for defining a specific signal, such as cos(t) or sin(t). Instead the instantaneous phase is only dependent of the local variation of the signal. For example, it assumes the value 0 at the maximal points of both cos and sin functions.

To see that the last statement is true: f(t)=cos(t) gives the corresponding analytic signal eit and the instantaneous phase is φ = t + 2πN, assuming that N is chosen such that φ lies in the range [0,2π[. Clearly, the value of φ is 0 at the maximal values of f. Now, set f(t)=sin(t) which gives the corresponding analytic signal -i e^{i t} = e^{i (t - \frac{\pi}{2})} . The instantaneous phase is \phi = t - \frac{\pi}{2} + 2 \pi N . The maximal values of sin(t) happens when t = \frac{\pi}{2} + 2 \pi M , i.e., when φ = 0 + 2π(N + M). Again, this gives φ = 0 at the local maxima.

My intention with this article is to describe this particular instantaneous phase. The other phase-related concepts should be in the Phase disambiguation page, but the earlier version of this article was missing a link to that page. --KYN 20:11, 1 July 2007 (UTC)

[edit] Why does Phase Unwrapping end up here?

Phase unwrapping is an interesting problem which has oodles of both potential and realized algorithms.

Why is it a redirect to this article, which contains almost zero information on phase unwrapping algorithms? cojoco (talk) 04:16, 3 January 2008 (UTC)

When someone writes the article you envision, it will replace the redirect.
--Bob K (talk) 05:23, 3 January 2008 (UTC)