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Harr Wavelet Question

  1. Apr 9, 2013 #1
    1. The problem statement, all variables and given/known data
    I think this may be a simple problem, but I really have no idea if I did it right because it seemed to easy.

    Here's the question, consider the Harr Wavelet [itex]\psi[/itex][itex]^{}_n{}[/itex][itex]_,{}[/itex][itex]_k{}[/itex](x) = 2[itex]^n{}[/itex][itex]^/{}[/itex][itex]^2{}[/itex]*[itex]\psi[/itex](2[itex]^n{}[/itex]x-k) where [itex]\psi[/itex] is the mother wavelet.

    Prove that [itex]\psi[/itex][itex]^{}_2{}[/itex][itex]_,{}[/itex][itex]_1{}[/itex] and [itex]\psi[/itex][itex]^{}_2{}[/itex][itex]_,{}[/itex][itex]_0{}[/itex] are orthogonal.

    2. Relevant Equations

    The mother wavelet of a Harr wavelet is a piecewise function that says

    [itex]\psi[/itex](x) = 1 if 0<=t<1/2
    -1 if 1/2 <= t <= 1
    0 otherwise

    3. The attempt at a solution
    I plugged in the n and k values that we are meant to prove, and found that we get
    [itex]\psi[/itex](4x-1) and [itex]\psi[/itex](4x)

    Graphing these functions show that they are both clearly integrated to zero, so is this proof that they are orthogonal?
  2. jcsd
  3. Apr 9, 2013 #2
    Two functions are orthogonal when their product integrates to zero.
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