I have some stumbling block in my thesis writing.

Do we use the same filter pair while implementing DWT filter bank with downsampling of the filter output, or filters do change also from level to level? Though on the Wiki page and in the book "Biosignal and Medical Image Processing, 3rd edition" by J. L. Semmlow and B. Griffel there are same labelling of filters at each decomposition level on the filter bank schemes:

Wavelets_Filter_Bank3.png

dwt.png ,

the description in Wikipedia states: "The filter output of the low-pass filter g in the diagram above is then subsampled by 2 and further processed by passing it again through a NEW low- pass filter g and a high- pass filterh with half the cut-off frequency of the previous one.."(c)

This resulted in big confusion for me. Logically, as I have been thinking before, for DWT we "travel" in frequency domain by signal downsampling and leaving the filters untouched (while e.g. in Stationary Wavelet Transform it is achieved through upsampling the filters themselves without signal modification). The word "new" in Wiki frustrated me a lot.

Please, help me to resolve this issue.

With respect,

-Andrey.

Yes, the taps are the same. Perhaps what is meant by "new" is that it runs at a different rate, and so has a different bandwidth (half) relative to the original input rate.

I think the word NEW is poor choice.  From the diagrams it looks like it's the same filters.  I'm not familiar with how this works, but since the output has the same number of taps as the input, the down sample by 2 is not really down sampling is it?  It's more like copying the data over itself so half is lost and half is duplicated.  I suspect that if you can explain to me how the filter is supposed to work, you will understand it way better than I ever will.

Mike

Andrey-

Have you thought about contacting the Wikipedia author and asking whether the "new" terminology should be changed to say "repeated", "updated", or as the case may be, to more precisely describe the process ?  Typically authors are listed by contribution, edit, etc and have an e-mail address.

Alternatively, once you're sure of what's going on, you can sign in and edit the article yourself.  If nobody complains, then at least theoretically your mod is deemed correct and a clarifying improvement.

-Jeff