Talk:Cohen–Daubechies–Feauveau wavelet

message: Interleave and filter is not going to work. If I had to implement it efficiently, I would use lifting. But for the exposition here the first variant has to be applied, as it is explained in Fast wavelet transform.--LutzL 09:54, 16 March 2006 (UTC)
replies: text: Hi, I added some headlines, so that one can edit in pieces. Of course You are right, I didn't understand the operation behind the word. If You check the "reconstruction" section in the "fast transform" piece, the abstract formula is exactly that, upsample, filter, add. By the way, the whole wavelet thing here is a total mess. The Discrete wavelet transform has less mathematical contents than the fast transform, lifting is still missing. The continuous wavelet transform is both mentioned in wavelet series, where it doesn't belong, and in wavelet, where it has too much detail, in fact more than in its own article. The latter should be a link to wavelet theory, which should be an overview with hardly more than short explainations of the list of wavelet-related transforms and the lists already present, :commons:wavelet and :commons:Category:wavelets are better organized;-). "discrete wavelet" should be an overview as well, linking together MRA, FWT, complex extension of both, the different classes ("haar", "daubechies", "coiflet", "biorthogonal") etc. Its all here, but in bad shape.--LutzL 19:05, 17 March 2006 (UTC)

text: Hello, it was a while :)  Yeah, synthesis filters are a little confusing, since they can be applied two ways (and there are two forms of them, respectively). At analysis/decomposition, you simply filter the data with a lowpass filter (phase 0) and a highpass filter (phase 1). But at synthesis/recomposition, you can either go with the upsample-filter-add, or the interleave-filter methods. The first one inserts 0s into both the coarse and the detail subbands, filters them with a lowpass and highpass filter, and adds them up. The second one interleaves the coarse and detail subbands, and filters it with a lowpass filter (phase 1) and a highpass filter (phase 0). The two methods, of course, produces the same result, and their filter pairs can be calculated from the other pair. Unfortunately the entire scientific literature regarding wavelets are excessively mystified, even at such simple things (At the moment I'm stuck with the directional filter bank part of the contourlet transform. Now, that's some difficult stuff). Frigo 21:34, 20 August 2007 (UTC)
thread_title:  The meaning of "Interleave" 

message: The expression for Q_2(X) is wrong and does not satisfy the identity 
(1-X/2)^A \, Q_A(X)+(X/2)^A\,Q_A(2-X)=1.
This identity implies Q_A(0)=1 and Q_A(1)=2^{A-1} so that Q_2(1)=2. The correct expression is Q_2(X)=1+2(X/2)=1+X.  —Preceding unsigned comment added by 71.36.189.68 (talk) 18:10, 4 February 2010 (UTC)
replies: text: Yes, you are right and it is a pity that it took over a year to correct. Must have flown under my radar at the time. (Not to mention that it was my error to begin with, 9/7 was done with CAS, why not 5/3?) Hopefully, not to many students were confused by WP-dependend teachers.--LutzL (talk) 11:52, 10 May 2011 (UTC)
thread_title:  something wrong in <math>Q_2(x)</math> 

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thread_title:  External links modified 

message: What wavelet is used in the example transform? 9/7 irreversible?
Lahebo (talk) 20:20, 8 February 2018 (UTC)
thread_title:  Figure description