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Math Help - foorier series from haar function..

  1. #1
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    foorier series from haar function..

    http://mathworld.wolfram.com/HaarFunction.html
    f(x)=  {1, 0<=x<3/4}
    f(x)=  {1, 3/4<=x<=1}
    calculate the foorier function with haar group
    here is the solution:
    L_0=\phi_{0,-1}(x)=1\\
    L_1=\phi_{0,0}(x)=\begin{Bmatrix}1,0\leq x\leq 0.5<br />
\\ <br />
-1,-0.5\leq x\leq 1<br />
end{Bmatrix}\\
    i dont know why i have latex error here the code is
    e_1=\phi_{0,0}(x)=\begin{Bmatrix}1,0\leq x\leq 0.5
    \\
    -1,-0.5\leq x\leq 1
    end{Bmatrix}\\
    aL_0+bL_1\\
    e_2=\phi{0,1}(x)\\
    e_3=\phi{1,1}(x)\\
    f=0.75\phi_{0,-1}(x)+1/4\phi_{0,0}(x)+1/2sqrtof2\phi_{1,1}(x)\\
    <f,e_0>=\int_{0}^{1}fe_0dx


    i dont know how they chose which haar function to take for the basis of of this serires
    i could say that i take haar function with n=10
    so my j=0..2^10
    and i whould have much more e's

    how they chose what haar sections to take as the orthonormal group
    ?
    Last edited by transgalactic; May 16th 2010 at 07:25 AM.
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  2. #2
    MHF Contributor
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    i have changed the function
    there was a mistake
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