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As is the case with most engineering topics, this is dense in terminology bordering on buzzword-iness and unnecessary complication in order to sound "mathy." As a mathematician, let me tell you that engineers are the butt of our jokes for this reason. —Preceding unsigned comment added by 69.212.51.181 ( talk) 22:59, 20 September 2008 (UTC)
Is this sentence for real?
- dcljr 07:07, 4 Sep 2004 (UTC)
Okay, I did a little research and I see there is a connection to the HUP. The way it's mentioned in this article made it seem like a spurious reference. Whatever... - dcljr 03:11, 5 Sep 2004 (UTC)
Heisenberg uncertainty is a physics thing and has nothing to do with wavelet (or Fourier) transforms. What's needed is the equivalent to the Nyquist–Shannon sampling theorem, I think. -- David Cooke 21:03, 6 July 2006 (UTC)
Hmmm... It's a tricky one the HUP really refers to Quantum Mechanics / QFT. And the article it is right in that sense. And again it's true that this is often stated as one reason for "turning to wavelet analysis". However, in reality (and for applied areas), like has been stated the Nyquist-Shanon sampling rate is key, I.e. that bandwidth limited signals can be represented perfectly given they are sampled at a sufficiently fine rate. From a Physics point of view (and I guess more generally in a theoretical statistics PoC) the point in the article is fine. Though perhaps the article should stress that? Personally I think there should be more of a statistics slant on this article, wavelets are of growing importance in the subject, a mention or discription of non-parametric signal estimation. For those reading with no background in the area, it basically means if you do a DWT of some signal, say a vector <X>, you get back a set of discrete wavelet coefficients, say <d_{j,k}>, basically then you threshold the coefficients (so a cofficient is less than some limit set it to 0, or keep it as it is otherwise). Doing the inverse transform gives a "noise free" representation of the signal. —Preceding unsigned comment added by 62.30.156.106 ( talk) 17:04, 7 February 2008 (UTC)
merge wavelet and wavelet transform? pretty related... - Omegatron 20:15, Sep 29, 2004 (UTC)
In my last edit, I formulated a distinction between a wavelet transform, which acts on functions or continuous signals, and its implementation in the fast wavelet transform via filter banks, which acts on coefficient sequences.-- LutzL 06:56, 31 May 2005 (UTC)
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)
|
Just to warn you, I have already made two major sets of corrections to this page (the first in July 2004) and they have since evolved back into incorrect forms. I do not think it is worth being rigorous or careful in Wikipedia articles as your hard work will only be undone by someone who doesn't know what they're talking about. Just go for a rough guide (i.e. minimal maths) on the main page and give references to relevant books and papers that will discuss things properly and have been peer reviewed by accomplished individuals. It may be worth being more rigorous on side pages (my definitions of continuous wavelets are still intact, for example). - Jon Harrop (Masters, PhD and job in wavelets).
The only sticking point of your program IMHO is that, you assume non-academics need to understand wavelets. They donot have to know it, and if you water down the quality of an article, it would turn off people. Wikipedia mathematics sections are quite technical, but donot compromise on the same "make lay person understand it" mission. I would suggest we maintain wavelet article upto good technical quality, and also have a short 1-2 paragraph introduction about applications of wavelets. I think most people are not able to understand wavelets without having any idea of transforms or signal processing. We shouldn't be wasting much valuable time arguing on this, IMHO. --Parasakthi ( பராசக்தி ) 15:04, 14 April 2009 (UTC)
Can a wavelet be any kind of time-limited oscillation? If you just generate a sinusoid and multiply it by a cosine window unrelated to any kind of transform, is that considered a wavelet, too?
Mastomer ( talk) 13:43, 20 January 2013 (UTC)
Is it possible to distill this discussion down and give a yes or no answer to the original question? That is: Can a wavelet be any kind of time-limited oscillation? Apologies, but I get a bit lost in some of the technical discussion, here. I'm also wondering if a sinusoid multiplied by a square function, so giving a finite duration sinusoid without tapering, can be considered to be a "wavelet". If so, then the opening sentence would have to be revised. Thanks, Isambard Kingdom ( talk) 14:54, 14 August 2016 (UTC)
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.
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)
On Mother wavelets, these are the functions that are "stretched" and "moved", in the Orthogonal case lets say you have two wavelet coefficients, you calculate the "inner product" between those two points and the first two points (x(1) and x(2)) in your data vector, then "shift" your wavelet you calculate the inner product of those too coefficients against x(3) and x(4)...and so on, that your first "finest resolution level". Next you stretch your wavelet so now you might have four wavelet coefficients, you you calculate the inner product of those against x(1):x(4), and so on, you do this for as along as you can, and you have your wavelet transform (discrete). So the mother wavelet is the non-shifted non-scaled "starting" wavelet. —Preceding unsigned comment added by 62.30.156.106 ( talk) 17:18, 7 February 2008 (UTC)
Using wavelet theory. Does anyone know what the second half of this para means? Im sure there's some useful info there if someone can bring it out by explaining more simply.-- Light current 20:51, 28 September 2005 (UTC)
WTF are L^1 and L^2? Why assume that the reader has seen this as "L" before?
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/?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.
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?
They are generally introduced as orthonormal transforms (well at least that's how I was introduced to them), but in reality the effects of shift invariance. So for example in statistics the MODWT and NDWT (Maximum Overlap, Non-Decimated respectively) transforms are often prefered. —Preceding unsigned comment added by 62.30.156.106 ( talk) 17:23, 7 February 2008 (UTC)
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:
-- LutzL 14:31, 24 April 2006 (UTC)
I'd appreciate a reference or proof sketch for the following claim:
A sufficient condition for the reconstruction of any signal x of finite energy by the formula
is that the functions form a tight frame of .
Thanks. -- Reza Rob 03:31, 4 January 2007 (UTC)
Proof. The definition of tight frame gives
for any . By using this equation for with , we get
On the other hand, we have
and using the definition again, we infer
for any . Now an application of the Riesz representation theorem completes the proof. Temur 16:30, 7 June 2007 (UTC)
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 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)
... 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)
So, if I'm reading the introduction to this article correctly, a wavelet is a pulse? That's what I think it says; 'starts at zero, rises, falls to zero again'; a pulse, right? So doesn't that description conflict with the subsequent comparison with seismic waves, or EKG, where the amplitude crosses back and forth across zero? Am I again proving to be just too psychically incompetent to correctly divine what's trying to be said? Trigley ( talk) 13:50, 7 June 2009 (UTC)
The head section starts out with a long comparison of wavelets to musical notes. While this might be useful for understanding wavelets I don't think the head section is the place for it. A dedicated section after a more formal introduction would be more appropriate. Ben T/ C 10:40, 26 April 2010 (UTC)
A wavelet is a wave-like oscillation with an amplitude that starts out at zero(0), increases, and then decreases back to zero.
A set of "complementary" wavelets will deconstruct data without gaps or overlap so that the deconstruction process is mathematically reversible.
In formal terms, this representation is a wavelet series representation of a square-integrable function with respect to either a complete, orthonormal set of basis functions, or an overcomplete set or frame of a vector space, for the Hilbert space of square integrable functions.
Mastomer ( talk) 13:19, 20 January 2013 (UTC)
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)
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)
Agreed. A sentence in the history section about the origin of (the French for) "wavelet" should suffice. Vaughan Pratt ( talk) 06:11, 7 November 2013 (UTC)
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.
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![]() | This article links to one or more target anchors that no longer exist.
Please help fix the broken anchors. You can remove this template after fixing the problems. |
Reporting errors |
As is the case with most engineering topics, this is dense in terminology bordering on buzzword-iness and unnecessary complication in order to sound "mathy." As a mathematician, let me tell you that engineers are the butt of our jokes for this reason. —Preceding unsigned comment added by 69.212.51.181 ( talk) 22:59, 20 September 2008 (UTC)
Is this sentence for real?
- dcljr 07:07, 4 Sep 2004 (UTC)
Okay, I did a little research and I see there is a connection to the HUP. The way it's mentioned in this article made it seem like a spurious reference. Whatever... - dcljr 03:11, 5 Sep 2004 (UTC)
Heisenberg uncertainty is a physics thing and has nothing to do with wavelet (or Fourier) transforms. What's needed is the equivalent to the Nyquist–Shannon sampling theorem, I think. -- David Cooke 21:03, 6 July 2006 (UTC)
Hmmm... It's a tricky one the HUP really refers to Quantum Mechanics / QFT. And the article it is right in that sense. And again it's true that this is often stated as one reason for "turning to wavelet analysis". However, in reality (and for applied areas), like has been stated the Nyquist-Shanon sampling rate is key, I.e. that bandwidth limited signals can be represented perfectly given they are sampled at a sufficiently fine rate. From a Physics point of view (and I guess more generally in a theoretical statistics PoC) the point in the article is fine. Though perhaps the article should stress that? Personally I think there should be more of a statistics slant on this article, wavelets are of growing importance in the subject, a mention or discription of non-parametric signal estimation. For those reading with no background in the area, it basically means if you do a DWT of some signal, say a vector <X>, you get back a set of discrete wavelet coefficients, say <d_{j,k}>, basically then you threshold the coefficients (so a cofficient is less than some limit set it to 0, or keep it as it is otherwise). Doing the inverse transform gives a "noise free" representation of the signal. —Preceding unsigned comment added by 62.30.156.106 ( talk) 17:04, 7 February 2008 (UTC)
merge wavelet and wavelet transform? pretty related... - Omegatron 20:15, Sep 29, 2004 (UTC)
In my last edit, I formulated a distinction between a wavelet transform, which acts on functions or continuous signals, and its implementation in the fast wavelet transform via filter banks, which acts on coefficient sequences.-- LutzL 06:56, 31 May 2005 (UTC)
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)
|
Just to warn you, I have already made two major sets of corrections to this page (the first in July 2004) and they have since evolved back into incorrect forms. I do not think it is worth being rigorous or careful in Wikipedia articles as your hard work will only be undone by someone who doesn't know what they're talking about. Just go for a rough guide (i.e. minimal maths) on the main page and give references to relevant books and papers that will discuss things properly and have been peer reviewed by accomplished individuals. It may be worth being more rigorous on side pages (my definitions of continuous wavelets are still intact, for example). - Jon Harrop (Masters, PhD and job in wavelets).
The only sticking point of your program IMHO is that, you assume non-academics need to understand wavelets. They donot have to know it, and if you water down the quality of an article, it would turn off people. Wikipedia mathematics sections are quite technical, but donot compromise on the same "make lay person understand it" mission. I would suggest we maintain wavelet article upto good technical quality, and also have a short 1-2 paragraph introduction about applications of wavelets. I think most people are not able to understand wavelets without having any idea of transforms or signal processing. We shouldn't be wasting much valuable time arguing on this, IMHO. --Parasakthi ( பராசக்தி ) 15:04, 14 April 2009 (UTC)
Can a wavelet be any kind of time-limited oscillation? If you just generate a sinusoid and multiply it by a cosine window unrelated to any kind of transform, is that considered a wavelet, too?
Mastomer ( talk) 13:43, 20 January 2013 (UTC)
Is it possible to distill this discussion down and give a yes or no answer to the original question? That is: Can a wavelet be any kind of time-limited oscillation? Apologies, but I get a bit lost in some of the technical discussion, here. I'm also wondering if a sinusoid multiplied by a square function, so giving a finite duration sinusoid without tapering, can be considered to be a "wavelet". If so, then the opening sentence would have to be revised. Thanks, Isambard Kingdom ( talk) 14:54, 14 August 2016 (UTC)
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.
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)
On Mother wavelets, these are the functions that are "stretched" and "moved", in the Orthogonal case lets say you have two wavelet coefficients, you calculate the "inner product" between those two points and the first two points (x(1) and x(2)) in your data vector, then "shift" your wavelet you calculate the inner product of those too coefficients against x(3) and x(4)...and so on, that your first "finest resolution level". Next you stretch your wavelet so now you might have four wavelet coefficients, you you calculate the inner product of those against x(1):x(4), and so on, you do this for as along as you can, and you have your wavelet transform (discrete). So the mother wavelet is the non-shifted non-scaled "starting" wavelet. —Preceding unsigned comment added by 62.30.156.106 ( talk) 17:18, 7 February 2008 (UTC)
Using wavelet theory. Does anyone know what the second half of this para means? Im sure there's some useful info there if someone can bring it out by explaining more simply.-- Light current 20:51, 28 September 2005 (UTC)
WTF are L^1 and L^2? Why assume that the reader has seen this as "L" before?
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/?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.
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?
They are generally introduced as orthonormal transforms (well at least that's how I was introduced to them), but in reality the effects of shift invariance. So for example in statistics the MODWT and NDWT (Maximum Overlap, Non-Decimated respectively) transforms are often prefered. —Preceding unsigned comment added by 62.30.156.106 ( talk) 17:23, 7 February 2008 (UTC)
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:
-- LutzL 14:31, 24 April 2006 (UTC)
I'd appreciate a reference or proof sketch for the following claim:
A sufficient condition for the reconstruction of any signal x of finite energy by the formula
is that the functions form a tight frame of .
Thanks. -- Reza Rob 03:31, 4 January 2007 (UTC)
Proof. The definition of tight frame gives
for any . By using this equation for with , we get
On the other hand, we have
and using the definition again, we infer
for any . Now an application of the Riesz representation theorem completes the proof. Temur 16:30, 7 June 2007 (UTC)
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 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)
... 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)
So, if I'm reading the introduction to this article correctly, a wavelet is a pulse? That's what I think it says; 'starts at zero, rises, falls to zero again'; a pulse, right? So doesn't that description conflict with the subsequent comparison with seismic waves, or EKG, where the amplitude crosses back and forth across zero? Am I again proving to be just too psychically incompetent to correctly divine what's trying to be said? Trigley ( talk) 13:50, 7 June 2009 (UTC)
The head section starts out with a long comparison of wavelets to musical notes. While this might be useful for understanding wavelets I don't think the head section is the place for it. A dedicated section after a more formal introduction would be more appropriate. Ben T/ C 10:40, 26 April 2010 (UTC)
A wavelet is a wave-like oscillation with an amplitude that starts out at zero(0), increases, and then decreases back to zero.
A set of "complementary" wavelets will deconstruct data without gaps or overlap so that the deconstruction process is mathematically reversible.
In formal terms, this representation is a wavelet series representation of a square-integrable function with respect to either a complete, orthonormal set of basis functions, or an overcomplete set or frame of a vector space, for the Hilbert space of square integrable functions.
Mastomer ( talk) 13:19, 20 January 2013 (UTC)
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)
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)
Agreed. A sentence in the history section about the origin of (the French for) "wavelet" should suffice. Vaughan Pratt ( talk) 06:11, 7 November 2013 (UTC)
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.