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Wavelets Analysis

  1. Apr 26, 2010 #1
    1. The problem statement, all variables and given/known data
    Given the following [tex]p_k[/tex] scaling coefficients and the following wavelet relations, find all four filters corresponding to these coefficients: low-pass decomposition, high-pass decomposition, low-pass reconstruction, and high-pass reconstruction.

    2. Relevant equations
    [tex]\phi (x)= p_0\phi (2x) + p_1\phi (2x-1) + p_2\phi (2x-2) + p_3\phi (2x-3)[/tex]
    [tex]\psi (x)=p_3\phi (2x+2) - p_2\phi (2x+1) + p_1\phi (2x) - p_0\phi (2x-1)[/tex]

    3. The attempt at a solution
    I just need help knowing how to start this problem. I've been looking throughout my book for the equations of the filters. I don't really understand how to design the filters from the wavelet relations.
  2. jcsd
  3. Nov 15, 2011 #2
    Does anyone know if i can construct-compose time-series consist of wavlets? e.g. if i have as data a characteristic wave height and a wave length i can produce time-series with Fourier transform which equals of a superposition of sinus waves. i want to do the same but with wavelets. possible?
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