Can anyone point me to literature that explains a quote from here : Why is a wavelet transform implemented as a filter bank?

So not all wavelets can be implemeted perfectly (invertible) with efficient filter banks. It is well known that discrete orthogonal wavelets cannot be real/symmetric/finite-length, except the Haar wavelet. Yet there exists a great deal of discrete wavelets that can be effciient on several signal/image/point cloud/mesh data.

~ Aug 25 '15 at 11:49 Laurent Duval

  • $\begingroup$ Hi Haarp, not quite sure what you need to have explained, specifically? Is it about what the Haar wavelet is, or why discrete orthogonal wavelets cannot be real, or symmetric, or is it about what efficient filter banks are? $\endgroup$ Feb 28 '19 at 12:43
  • $\begingroup$ Thanks for the reply, I am not sure why cannot discrete orthogonal wavelets be real, do they need to be complex and why ? I have achieved perfect reconstruction with a length 2 filter w=[1,1](symmetric ?), which I have used to create a set of filters for analysis and synthesis as quadratic mirror filters. If I try any other size for the wavelet or values that are not the same i get lots of distortion and can go one level of decomposition maximum, as with the first wavelet mentioned I can easily go 8 levels deep. $\endgroup$
    – haarp
    Feb 28 '19 at 12:55
  • $\begingroup$ Please edit your post to include the exact question you'd like to ask – that makes it far more likely someone will stumble across your question and be like "ooooh, that's interesting, let's do this!". $\endgroup$ Feb 28 '19 at 13:04

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