Talk:Wavelet
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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)
- I agree; this article starts off with non-useful generalizations and then goes into theoretical math that seems either obfuscated or not written by someone's who ever created a practical implementation of a wavelet. Was someone just summarizing a math textbook? I even understand FFTs, but this article did not help me to understand wavelets. It seems to be some technique of DSP in the time domain, but it's utterly incomprehensible beyond that. Math for the sake of math is not helpful.
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Is this sentence for real?
- The wavelets forming a CWT are subject to Heisenberg's uncertainty principle and, equivalently, discrete wavelet bases may be considered in the context of other forms of uncertainty principle.
- 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)
- The same thing applies to the STFT as well. It is pretty important, though I don't really understand it. Apparently it means that you can't measure the instantaneous freuqency of a signal. See Talk:STFT - Omegatron 17:12, July 18, 2005 (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)
- Actually, the Heisenberg uncertainty principle is mentioned in wavelet literature, and as discussed, it is a lot less mysterious than what has been presented in popular physics literature. As Omegatron says, it does deal with the fact that there is no such thing as "instantaneous frequency" and its actually a very important consideration no matter what type of analysis you consider (Wavelet or Fourier). The time/frequency representation utilized depends upon the type of signal you are looking for.
- Hmmmm, but maybe the literature is wrong. On this page on Wavelet.org someone claims that the Uncertainty Principle of analysis and the Heisenberg Uncertainty Principle are indeed different. But the explanations I've read tend to have (IIRC) similar if not the same formalizations. Perhaps this is just getting into the nitty-gritty semantics and connotation of the Uncertainty Principle in signal analysis, whether it means just the formalization (which from my very uneducated eyes appears to be related to the related and derived Robertson-Schrödinger relation) or that of the original mathematical theory derived by Heisenburg without the implications of the physics involved. ATM, I'm only using the wikipedia article (as reference) on or HUP or UP, which also globs it all into the same article.
- I feel like Clinton here.... 'It depends upon what your definition of "IS" is.' Root4(one) 21:37, 18 November 2006 (UTC)
- Mallat's "A wavelet tour of signal processing", p.31 claims: Theorem 2.5 (Heisenberg Uncertainity): The temporal variance and the frequency variable of
satisfy
. I think the reference is pretty kosher. - Sesse 23:10, 4 December 2006 (UTC)
- Mallat's "A wavelet tour of signal processing", p.31 claims: Theorem 2.5 (Heisenberg Uncertainity): The temporal variance and the frequency variable of
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)