We have unnormalized Haar matrix which, is for example,

H4=[1 1 1 1;1 1 -1 -1;1 -1 0 0;0 0 1 -1]

After normalizing it, we use for haar transform. I know how to produce it using kronecker product. Can we generate other unnormalized wavelet family matrixes? For example, how can I generate unnomalized Daubechies or symlet matrixes?


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    $\begingroup$ There's no general shortcut for the Wavelets other than Haar. You have to go through the dyadic decomposition and construct the basis vectors from the definition of the decomposition. $\endgroup$ – Jazzmaniac Jul 6 '15 at 13:16
  • $\begingroup$ @Jazzmaniac Can u please give me matlab example code for symlet? $\endgroup$ – Haybert Markarian Jul 6 '15 at 13:31
  • $\begingroup$ I don't have such code. Writing code for wavelet decomposition is not terribly hard, but still a quite a bit of work. I'd suggest you pick up a textbook and work through it step by step. That's the best way to really understand something. $\endgroup$ – Jazzmaniac Jul 6 '15 at 15:15
  • $\begingroup$ @Jazzmaniac I have written wavelets decomposition and construction codes for all wavelet families based on its block diagram which uses filter banks and does downsampling in columns and rows and it works well but I dont get what you exactly mean by saying '' basis vectors '' ?? $\endgroup$ – Haybert Markarian Jul 6 '15 at 17:53
  • $\begingroup$ Like any linear bijection (i.e. 1-to-1-map), the discrete wavelet transform can be regarded as a basis change. The basis vectors you change into are the row vectors of the transformation matrix. $\endgroup$ – Jazzmaniac Jul 6 '15 at 19:11

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