Talk:Morlet wavelet

Fourier transform

While the definition of the wavelet itself seems to be ok, I have serious doubts about the fourier-transform stated in the article. Unfortunately, the article does not state any source for anything, and the definition according to which the admissibility-constant was calculated remains unclear. 134.176.25.80 14:51, 30 January 2007 (UTC)

I've rewritten the Fourier Transform in a clearer format. You can see how each term derives from those in the wavelet itself. The admissibility criterion is the conventional one. I've added referenced to the original work but there is a much clearer explanation in my PhD thesis. Jon Harrop 04:24, 11 April 2007 (UTC)

I'd suggest to fix the definitions of the wavelet and its spectrum so as to match those in Ingrid Daubechies's "Ten lectures on wavelets". As for the admissibility-constant and central frequency, I'm not sure, but maybe someone else can state a reliable source for them? 134.176.25.80 14:51, 30 January 2007 (UTC)

This page was taken from my PhD thesis. For complete definitions please refer to that.

Daubechies always concentrated on discrete wavelets and transforms so her stuff never really covers continuous wavelets and time-frequency analysis (which is the main use of the Morlet wavelet). Torresani et al. give good coverage of this.

You can get an idea of the functional form of the Fourier transform of the Morlet wavelet by breaking it into the sum of a Gaussian and a Gaussian-modulated plane wave before doing the transform. The expression given here is probably correct but could be rewritten more elegantly.

As User:Requestion keeps deleting my content I have no incentive to write for Wikipedia now. If you want accurate information I suggest you look up the links that were deleted as spam (e.g. my thesis). Jon Harrop 04:31, 9 April 2007 (UTC)

How on god's green earth do you work out the integral to get the Fourier transform?— Preceding unsigned comment added by 128.244.71.33 (talk • contribs) 19:13, 16 July 2007

Expert

Why has this article been marked as being in need of expert attention? Jon Harrop 04:11, 11 April 2007 (UTC)

The Morlet wavelet was superceded by the Hilbert-Hermitian wavelet

The reference for this statement is [http:// www.ffconsultancy.com/free/thesis.html my PhD thesis]. To avoid a conflict of interests, I'll let someone else reference me. Jon Harrop 08:25, 12 April 2007 (UTC)

This isn't a suitable source. It maybe true (I don't have reasons to mistrust you), it hasn't yet entered the realm of established knowledge. For that secondary sources have to enter the the scene. Encyclopedias aren't a biotoipe for innovation. --Pjacobi 09:42, 12 April 2007 (UTC)

My research is now old and has since been adopted by groups all over the world including the USA, Canada, Australia, Britain, Norway, Switzerland, Finland and Japan. Here are some example papers (note that I was not involved in the papers that list me as a co-author; they simply used my software):

Silver transport in GexSe1−x:Ag materials: Ab initio simulation of a solid electrolyte by De Nyago Tafen, M. Mitkova and D. A. Drabold, Phys. Rev. B 72, 054206 2005

Structural characteristics of positionally-disordered lattices: relation to the first sharpdiffraction peak in glasses by J. K. Christie, S. N. Taraskin, and S. R. Elliott

Real and reciprocal space structural correlations contributing to the first sharp diffraction peak in silica glass by T. Uchino, J. D. Harrop, S. N. Taraskin, and S. R. Elliott, Phys. Rev. B 71, 014202 (2005)

A Wavelet Analysis of Medium-Range Order in Vitreous Silica by T. Uchino, J. D. Harrop, S. R. Taraskin, and S. R. Elliott at X International Conference on the Physics of Non-Crystalline Solids (Parma, Italy)

Rick Gustavsen from LANL in the USA recently asked me how I should be cited in a paper they are submitting to Appl. Phys. Lett.

Incidentally, I had already e-mailed the Wikipedia admins to get clarification on this (after Requestion vandalised much of my content) and they state that a PhD thesis is a valid self-citation provided it was was peer reviewed by experts. Jon Harrop 04:25, 13 April 2007 (UTC)

These aren't secondary source for proving that one Wavelet type is superceded by another. No argueing here on Wikipedia will change that. Just wait, for heavens sake! Either your innovation finds it ways into textbooks and review articles, or not. --Pjacobi 07:06, 13 April 2007 (UTC)

As the author of both a PhD thesis and about a dozen books, I can definitely say that a PhD thesis is much more rigorously reviewed by experts than a book. You should value the content of a thesis (especially one marked scholarly or one from Cambridge University) above that of a book. If it is the word superceded that you object to, I can add a description of how the Morlet wavelet is flawed (Goupillaud described this in his original paper) and how the Hilbert-Hermitian wavelet improves upon it (chapter 3 of my thesis). If you want another expert to verify this, you could try asking Paul Addison. Jon Harrop 22:00, 13 April 2007 (UTC)

Meta: I'm one of the more than thousands admins on enwiki, but that's totally unrelated. Admins don't have special say in content disputes. "Appealing to higher" (e-mailing the contact address, Jimbo, whoever) should be only be issued for legal issues. Nobody stops from doing it in other case, but it looks a bit silly. But you may want to ask at Wikipedia talk:WikiProject Mathematics to get more editors' attention. --Pjacobi 07:10, 13 April 2007 (UTC)

We contacted the admins about libellous accusations and they clarified the point about PhD theses in discussion. The point is, PhD theses also contain a lot more background and introductory material than a paper, so they are ideal citations for Wikipedia. If anyone wants to clarify this issue by contributing to the article, I don't mind if they take content from my PhD thesis. Jon Harrop 22:00, 13 April 2007 (UTC)

Hello Jon. Wikipedia is not a forum to be used for your self-promotion and personal glorification. There is a major WP:COI with the edits you are making. It also appears that you are engaging in original research which isn't allowed (WP:NOR). (Requestion 00:21, 14 April 2007 (UTC))

I just ran into this link [1] on the wavelet.org site. Is it dated April 12th and it is titled "Morlet wavelet superceded by the Hilbert-Hermitian wavelet." In this forum posting Jon appears to be promoting his ffconsultancy.com Mathematica CWT product. On the previous day Jon made the same superceded claim with this Wikipedia edit [2]. Is this some sort of advertising campaign that is attempting to leverage the "authority" established on Wikipedia? See Talk:Hilbert-Hermitian wavelet for more discussion pertaining to the WP:COI of this edit. (Requestion 05:38, 19 April 2007 (UTC))

In its current state, the wavelet.org discussion forum is dysfunctional and rarely a place to gain authority. Except perhaps as an advertisement spammer. The issues of the wavelet.org journal would be a different story.--LutzL 10:31, 19 April 2007 (UTC)

I was suggesting the reverse course of events. Jon adds the superceded claim to this Morlet article which establishes authority. Then the next day Jon begins advertising the superceded claim on the wavelet.org site. You know the saying "If Wikipedia says it is true then it must be true!" (Requestion 17:18, 19 April 2007 (UTC))

My PhD thesis is the authoritative source, not the current Wikipedia article. Jon Harrop 21:51, 2 May 2007 (UTC)

There are plenty of reasons to mistrust Jon Harrop. He has been engaging in a shameful self-promotion campaign on Wikipedia and this is just his latest ploy. For details see User_talk:Requestion/Archive_1#Jdh30_Warnings and User_talk:Jdh30 07:39, 12 April 2007. Note that the Jdh30 talk link is a direct date link because Jdh30 has blanked his talk page 3 times so far. Using yourself as a reference is a major WP:COI and like Pjacobi said it is not a WP:RS. (Requestion 16:14, 12 April 2007 (UTC))

Ok, you've got me. I confess. All of those people above are actually me. I created the Physical Review journals myself, as a marketting campaign to sell books on OCaml. I referenced my own PhD thesis and book while I was simultaneously in the UK, Egypt, Australia and Japan. I can do that because I know how to quantum tunnel. Jon Harrop 04:25, 13 April 2007 (UTC)

The shortcomings of Morlet's wavelet were described by Morlet himself in his original work. I have replaced the deleted content because it was cited and there is clearly no COI. Jon Harrop 01:36, 14 April 2007 (UTC)

This looks perfectly OK (to this extent this can be said, without an actual literatur search). Jon, please just stop mentioning your own work in the article, until it has become common knowledge in the field (and them, I suppose, you need not longer add it yourself). --Pjacobi 21:24, 14 April 2007 (UTC)

Given that I wrote all of these pages, it does not seem unfair for me to reference my own work when appropriate. Jon Harrop 21:52, 2 May 2007 (UTC)

Morlet Wavelet Plot

Regarding the plot provided with this subject, it does not contain an abscissa title, so it is unclear what the variable is. As the wavelet function appears to depend on both sigma and time, it should be specified which variable is actually varying.— Preceding unsigned comment added by 155.148.8.68 (talk • contribs) 01:36, 3 May 2007

Central Frequency

The formula and discussion of "central frequency" is wrong. From the formula for the Fourier Transform of the Morlet wavelet, it is clear that the peak is near omega=-sigma, NOT omega=+sigma as stated in the final line. The following formula for omega_Psi is also wrong; just differentiate the Fourier Transformed wavelet to see that.

Of course, there are many definitions of the FT. The one used here uses exp[+i omega t] in the kernel. If you use exp[-i omega t] instead, you get the same formula, but containing exp[-(sigma-omega)^2/2] instead of exp[-(sigma+omega)^2/2], and the peak is near omega=sigma.

Alternatively, if you want to stick with your FT formula, you need exp[-i sigma t] instead of exp[+i sigma t] in the original wavelet formula.

Pcally 01:11, 8 November 2007 (UTC)

Victor Signaevskyi: The formula is not true (as on me). My decission is based on the results, that I have got using MathCAD. When I tried to plot the function, given by the Author I have got another mother wavelet (the form of it lies near Paul wavelet) —Preceding unsigned comment added by 193.178.34.39 (talk) 20:10, 9 November 2009 (UTC)

Is it really a wavelet?

I use this wavelet all the time. Uncomfortably definition of the Morlet wavelet does not even satisfy the 1 of the basic properties of a wavelet, the area under the curve must be 0. Who ever made this page did it wrong. — Preceding unsigned comment added by Bigrockcrasher (talk • contribs) 15:52, 25 February 2011

Please explain. The value of the Fourier-Transform at frequency zero, which is a generalization of the "area under the curve", is indeed zero with the given choice of kappa. Or do you claim that the Fourier transform is wrong? This would require an extensive demonstration, since at first glance everything is right.--LutzL (talk) 17:01, 25 February 2011 (UTC)

Connections to human perception

I am not an expert on morlets, but I know a fair bit about human perception and I unaware of any connection between morlets and human perception (first paragraph of article). The citations do not seem to help. Morlets may been used to analyze data from perceptual experiments, but that is quite different from their being "closely related to human perception". I am not comfortable making the change myself, but strongly suggest this sentence be eliminated. (L Snyder, Washington University Anatomy & Neurobiology dept. -- 99.177.218.213 (talk) 03:06, 22 December 2013 (UTC)

Could You please review the citations given in the sentence. The first article (published 2005) contains the statement

The use of Gabor filters is motivated by information theoretic and biological facts. Gabor [6] showed that gaussian-modulated complex exponentials provide the best trade-off between spatial and frequency resolution. Neurophysiological studies show that visual cortex simple cells are well modeled by families of 2D Gabor functions [4]. Both facts raised considerable interest and suggest that neuronal structures may develop toward optimal information coding.

with reference to

[4] J.G. Daugman: Two-dimensional spectral analysis of cortical receptive field profiles. Vision Research, 20:847–856, 1980.

That quote may or may not be a reflection of the initial enthusiasm in the early days (1980) of wavelet analysis when all was new an shiny.

The second link appears inappropriate for this sentence. It contains some generalities about all the wavelet transforms (in that superior to the wikipedia wavelet articles) among them the observation that wavelets decompose signals of many origins into time-frequency atoms.--LutzL (talk) 09:44, 22 December 2013 (UTC)