Talk:Wavelet

message: Have merged in wavelet transform to this article.  I'm also attempting a revamp of the all the wavelet content on wikipedia as i feel there is a lot of missing information and not very easy to understand.  Having just completed a masters project on the subject (and knowing nothing about them when i started) i feel i'm in a good position to do this.
If anyone wants to help i've put together a list of what i think need doing (feel free to add to it).  In particular i don't have much knowledge on wavelets with continuous signals or complex wavelets so if someone could help with that.
Johnteslade 10:24, 15 July 2005 (UTC)
replies: text:  Just thinking out loud here. For a piecewise rectilinear function (e.g., an irregular saw-toothed function) defined over a finite domain, is there a dense, complete, orthonormal set of coordinate functions, also piecewise rectilinear, that can be used as basis for expansions?  —Preceding unsigned comment added by 69.158.109.40 (talk) 13:51, 7 October 2007 (UTC)
thread_title: Updating wavelet content

message: Having googled, I have found some wavelet definitions given as low-pass filterbanks, and I've found a definition of QMF for an even length filterbank (HP(n) = (-1)^n . LP(N-1-n), n = 0,1,...,N-1). But this could do with being included on this page or as another page called QMF. It would be nice to have a definition for an odd length filterbank too - I can't find that anywhere.
:Hi, QMF is not entirely correct, since it only applies, in the strict sense of the definition, to the Haar-Wavelet. Wavelet filter banks are CQF, conjugate quatrature filterbanks, since the analysis filterbank is the adjoint (wrt. the canonical hermitian structure on the spaces of discrete signals) to the synthesis filter bank. The difference, as I understand, is that in QMF, the same filters are used in analysis and synthesis, whereas in CQF, the analysis filters are time reversed wrt. the synthesis filters (and conjugate if complex).--LutzL 06:38, 5 September 2005 (UTC)
thread_title:  QMF (Quadrature Mirror Filterbank?) 

message: Any chance of anyone simplifying the mathematical jargon used in this para so normal people (like me) can understand It?--Light current 22:56, 27 September 2005 (UTC)
thread_title:  Mother Wavelet 

message: The "Wavelet based time-frequency analysis in Mathematica" external link is a link to a commercial for a small Mathematica worksheet that was placed on this page by the author of that worksheet. This presumably is a clear violation of the Wikipedia:What_wikipedia_is_not guidelines. Similar violations by the same author also have occurred in the OCaml and Ray_tracing articles, cf. the associated discussion pages. - Thomas Fischbacher
That link is to a tutorial page that demonstrates the application of time-frequency analysis to example signals from several classical subjects. The actual analyses are done using commercial products but the contents of the page are educational in their own right. Fischbacher's objections to my other contributions have now been ignored, perhaps because he has since abused them in an attempt to justify his unusual views by posting them on comp.lang.lisp (where they were also ignored). See MarkSweep's comments in the history of the OCaml article. - Jon Harrop
Gee. Thanks for putting in my name and that reference to my web page, Jon. I must admit that I initially did not bother, but maybe should have. But, even more thanks for actually changing your previous commercial link that pointed to the actual product salesblurb to a more neutral one:
http://en.wikipedia.org/w/index.php?title=Wavelet&diff=27016379&oldid=25759232
However, don't you *think* it's just a little bit dishonest to do so and nevertheless try to give the impression on this discussion page as if this link always had pointed to that other tutorial page, and not to the merchandising page? Well, actually, it's not overly clever, at least. Wikipedia has version control (see above), you know.
As for the links you provided, should someone really be interested, I'd advise some googling to get more context, which is bound to give interesting insights into other out-of-context-quoting and history re-writing.
-- T.F.
#Please sign your posts with four tildes, like this: ~~~~
#The external links section should be cleaned up and merged with the references section, i.e. have, author, title, date, at a minimum. This will discourage advert links. linas 17:38, 10 December 2005 (UTC)
thread_title:  Commercial Abuse 

message: From the article:
 In formal terms, this representation is a wavelet series, which is the coordinate representation of a square integrable function with respect
 to a complete, orthonormal set of basis functions for the Hilbert space of square integrable functions. Note that the wavelets in the JPEG2000
 standard are biorthogonal wavelets, that is, the coordinates in the wavelet series are computed with a different, dual set of basis functions.
Why bother to say that wavelets form an orthonormal basis, and then proceed to point out that there are wavelet families which are not orthogonal?
:Someone with the time to defend the changes could formulate that in most textbooks on wavelet theory there are only orthogonal wavelets. The theory of orthogonal wavelet series is, because of the relatively simple theory of orthonormal bases in separable Hilbert-spaces, much simpler than the theory of frames and stable bases that lies behind biorthogonal wavelets. But JPEG2000 is the most widely known application of wavelets, so a note of caution to the different nature of their wavelets should turn up in the introduction.--LutzL 09:31, 9 January 2006 (UTC)
replies: text: Wrong. Computer scientists use wavelets for signal coding and tend to stick to orthonormal wavelet bases and discrete wavelets. Scientists and engineers often used the continuous wavelet transform (not orthogonal) for time-frequency analysis. This is described in detail in my PhD thesis but I am not allowed to cite it (the link was deleted as spam) because I am affiliated with my own PhD thesis. I was going to fix the article but the Wikipedia admins just convinced me that it would be a waste of my time. If you want accurate information on this (or any other) subject, I suggest that you do not read Wikipedia. Jon Harrop 04:48, 9 April 2007 (UTC)
replies: text: Wrong to the square. The FBI fingerprint wavelet as well as the reference wavelets of JPEG2000, CDF 3/5 and 7/9, are biorthogonal. Computer scientists in image-processing prefer linear phase over orthogonality. For audio compression things are different, but then there is no widely known audio compression standard using wavelets. Wavelet based OFDM, where orthogonality is already in  the name, is a nice experiment, but has no widely used application at this time. Disclaimer: I do not live in Japan.--LutzL 07:31, 30 April 2007 (UTC)
thread_title:  Wavelets are not necessarily orthonormal 

message: Johnteslade announced something like that last year, there was lately some activity in restructuring content by HenningThielemann, believed to be identic to 134.102.210.237, but all not very convincing. I was giving someone on www.wavelet.org the advice to check the pages here for details of the wavelet theory. But had to admit (to myself) later that for someone that only know some calculus and wants a quick glance on how wavelet transforms are implemented, this information is unaccessibly hidden in the wikipedia-articles. So I would propose:
* To move this article to wavelet theory and 
** remove the focus on wavelet functions. Instead, it should be a short overview on the parts of wavelet theory.
** move and join the part of the continuous wavelet transform to its own article. It is ridiculous that this overview it has more detail on this topic than the specialized article.
* reformulate the discrete wavelet transform to be also an overview on this topic, 
** using wavelet basis and dual wavelet basis to explain orthogonal and biorthogonal wavelet transforms
** pointing out that most practical transforms are constructed via a multiresolution analysis (MRA),
** that from this one gets a nice and fast implementation via the fast wavelet transform (FWT) algorithm.
** Then comes some difficult part where one should explain that working backwards from the requirements of the FWT one gets conditions on the filterbanks that can have solutions which also lead to a MRA. There should be an extra article Construction of wavelet scaling functions, which re-joins the theoretical contents of the orthogonal wavelet and biorthogonal wavelet articles.
** next come the links to the examples Haar wavelet, Daubechies wavelet, Coiffman wavelet etc. for orthogonal transforms and Cohen-Daubechies-Feauveau wavelet etc. for symmetric biorthogonal transforms.
*The article on the fast wavelet transform should be enhanced by ready-to-implement pseudocode for both orthogonal and biorthogonal transforms. Obviously, this code should be removed from the overview on diskrete wavelets.
--LutzL 14:31, 24 April 2006 (UTC)
thread_title:  Reorganization of the wavelet articles 

message: Shouldn't the Introduction actually do some "introducing" for the layman? It seems a little stilted in its language - it should be a broader statement with a brief description of the capabilities of Wavelet Theory.
::The use of continuous wavelets in science and engineering is covered in detail in my PhD thesis. This article is (was) a very cut down version of that. Refer to my thesis for a good introduction to that aspect of this subject. Jon Harrop 04:50, 9 April 2007 (UTC)
replies: text:  There should be a more accessible introduction in general, not only of the applications but what a wavelet is, why it is useful and how the transform works. Compare with the Introduction to wavelets paper.  The intro goes from general to specific, and so much becomes clear from the first 4 sentences!  -Pgan002 23:41, 29 April 2007 (UTC)
replies: text:  The best introduction to wavelets (IMO) is the MIT open ware course on Engineering mathematics that has video lectures. After that, really you want to get guidance from your academic supervisor. Wavelets theory is taught VERY differently depending on your subject area (wavelets know span everything from CS - Geography). This article is pretty technical, but saying that, it's pretty decent too.  —Preceding unsigned comment added by 62.30.156.106 (talk) 17:27, 7 February 2008 (UTC)
thread_title:  The Introduction 

message: The introduction asserts that wavelets divide a signal into different frequency components. This is incorrect. That's what Fourier analysis does. Wavelets cut up a signal into different "scale" components, not frequency. Frequency is only defined in terms of complex exponentials, any link between scales and frequencies is intuitive and heuristic, not precise. More information can be found at M.B.Priestly's 1995 paper titled "Wavelets and Time dependent spectral analysis".  —Preceding unsigned comment added by 203.167.251.186 (talk) 22:52, 8 January 2009 (UTC)
replies: text: Then why didn't you change it? It's a perfectly reasonable point. One could even say that a challenge in the design part of wavelet theory is to come up with transforms where the scale components behave approximately as frequency components. Note that a frequency component always spans a certain frequency range.--LutzL (talk) 12:14, 9 January 2009 (UTC)
thread_title:  Problem in Introduction 

message: ... at least, was as article in Scientific American specifically about wavelets. It was clear, and taught me enough to hold me for more than a decade. Sorry to say, I don't know when it was published, but Gerard Piel was alive and well, just about sure. Back then, Sci. Am. presumed that people had minimal difficulty reading and attention spans with durations of several minutes at least instead of (more likely) a few seconds at best. Nevertheless, graphics were not neglected.
Consider that most Wikipedia readers might not have any idea what "orthogonal" means, and fewer might think of lines in a plane that are at right angles. However, when one refers to orthogonal functions, you lose a lot of people.
Another source I found very helpful was the sample illustrations in the data sheet for an Analog Devices complex IC devoted (iirc!) to wavelet decomposition and reconstruction of images. It was most interesting to see, as graphic images, the different "levels" of wavelets created by wavelet analysis. (I'm probably mistaken in assuming similarity between decomposition and analysis.)
Of course, copyright is most important in Wikipedia, but what can't be copyrighted is an understanding and an approach to explaining a topic.
To the author[s], I'd say please try to keep in mind what a reader who is curious about the topic is likely to know. Sad to say, even Fourier transforms are probably something totally unfamiliar. ("What's an FFT?")
I had higher hopes of learning something more than I did.
The reason I came to this article was the BBC news item about Google using image similarity, also being aware of the Linux application imgSeek, which apparently uses wavelet decomposition of images (and similarity of the wavelets?) to locate similar images.
I'm pondering whether wavelets and solitons are related, btw.
I do wish you all well!
Regards, Nikevich (talk) 17:23, 21 April 2009 (UTC)
replies: text: Hi, You should probably read on under Discrete Wavelet Transform, which deals with image compression etc. Sadly, from a didactical point of view, the collection of wavelet articles is in a lamentable state, even if all the important technical information is present somewhere. Is "orthogonal" for "at right angles" really that esoteric? I thought that phrases like "orthogonal to reality" had entered popular culture. I'm not so sure about "perpendicular" as a synonym. It would be nice if You could find references for all your sources.--LutzL (talk) 07:57, 22 April 2009 (UTC)

text: No and yes. The theory of continuous wavelets allows for a wide class of functions to be basis functions. In practical applications a wavelet has compact support, i.e. it starts at zero, rises, oszillates a small number of times and then falls again to zero. The integral over all oszillations is zero. There are graphs of examples of widely used wavelets somewhere in the article.--LutzL (talk) 10:05, 8 June 2009 (UTC)
replies: text: I see your reasoning for modifying the introduction, but still feel your wording was too imprecise, even for a non technical definition. If it begins at zero and then oscillates is there any reason to say it increases and decreases also? Must amplitude always evoke modulation? Is "ripple" not a bit of a colloquialism? I propose the following; "Non-technically a wavelet is is a curve whose amplitude is zero on either side of a compact region of oscillation, similar to the pulses on a seismograph or ECG." Is this sufficiently descriptive and succinct for the layperson?  —Preceding unsigned comment added by 97.83.161.77 (talk) 16:31, 9 June 2009 (UTC)
thread_title:  A worthy source for non-mathematicians 

message: This article is too mathematical and doesn't explain someone who doesn't want to go into the details what "waveletS" are, why they return in so many contexts, and what the core ideas to hold onto are. Also, the fact that the title of the article is "Wavelet" instead of "Wavelets" is already a disappointment on its own: In reality, they're always called "Wavelets", and what interests me is what "Wavelets" are about, not what a single "Wavelet", which is a more detailed underlying mathematical concept, is.193.190.253.144 (talk) 22:09, 14 June 2010 (UTC)
replies: text: I'll agree that it's too mathematical, but they're kindof a pain to describe, so if you know how to improve it, by all means go ahead. They aren't always called wavelets, see for example the Haar wavelet. And I think the goal should be to describe both the underlying concept and how they're used - think of it like a broad overview article in line with Animal. VernoWhitney (talk) 22:22, 14 June 2010 (UTC)
thread_title:  Wavelet not in plural? 

message: What is the purpose of the section Wavelet#Name?  As acknowledged in Thomas Colthurst's 1997 MIT Ph.D. thesis, the word "wavelet" is over two centuries old, you can see it for example in Book VIII of Shelley's Queen Mab, "Like the vague sighings of a wind at even That wakes the wavelets of the slumbering sea", or in Coleridge's Literary Remembrances III, "You only hide it by foam and bubbles, by wavelets and steam-clouds, of ebullient rhetoric."  In seismology Seismic inversion#Wavelet estimation concerns the problem of resolving multiple seismic reflections of a pulse generated by an explosive charge in order to identify the surface(s) that the pulse bounced off.  In physics the constituent waves of a wave packet are sometimes referred to as wavelets, for example as in Nappo's An Introduction to Gravity Waves.
None of these uses, whether in poetry, physics, seismology, etc. have anything to do with using wavelet transforms to analyse an arbitrary signal as a sum of wavelets.  The fact that the word "wavelet" was in the English language (and presumably "ondelette" in French) centuries before the invention of the wavelet transform hardly seems to warrant even a remark, let alone an entire section, which furthermore conveys the impression that wavelets as treated in this article predate 1980, which is simply false. Vaughan Pratt (talk) 20:06, 6 November 2013 (UTC)
replies: text: What version of the article are you referring to? Once there was this questionable content that I was not innocent of. But the two sentences that stand now are, the way I read them, in accord with your arguments. One may merge them into the lede or into the history section, there is no mystery to solve in this name. Until proven otherwise, as mathematical object these functions were first introduced as "ondelettes" in french texts, with the translation of them into english they became, without further ado, "wavelets". But this is one of the minor problem of the whole wavelet section in wikipedia.--LutzL (talk) 22:05, 6 November 2013 (UTC)
thread_title:  Suggest deleting "Name" section 

message: The subsection on the applications of WNNs is closely paraphrased from https://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/AV0809/martinmoraud.pdf. The paper is open access but does not appear to have been released into the public domain. The same edit which contributed the text in question also contributed the first part of the WNN section, though I didn't find any suggestion this is also infringing from a quick search.
Frankplow (talk) 16:38, 17 October 2021 (UTC)
thread_title:  Close Paraphrasing in Applications of WNNs