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Homework Help: Foorier series from haar function

  1. May 16, 2010 #1
    http://mathworld.wolfram.com/HaarFunction.html
    [tex]f(x)= {1, 0<=x<3/4}[/tex]
    [tex]f(x)= {-1, 3/4<=x<=1}[/tex]
    calculate the foorier function with haar group
    here is the solution:
    [tex]L_0=\phi_{0,-1}(x)=1\\[/tex]
    [tex]L_1=\phi_{0,0}(x)=\begin{Bmatrix}1,0\leq x\leq 0.5
    \\
    -1,-0.5\leq x\leq 1
    end{Bmatrix}\\[/tex]
    i dont know why i have latex error here the code is
    L_1=\phi_{0,0}(x)=\begin{Bmatrix}1,0\leq x\leq 0.5
    \\
    -1,-0.5\leq x\leq 1
    end{Bmatrix}\\
    [tex]aL_0+bL_1\\[/tex]
    [tex]L_2=\phi{0,1}(x)\\[/tex]
    [tex]L_3=\phi{1,1}(x)\\[/tex]
    [tex]f=0.75\phi_{0,-1}(x)+1/4\phi_{0,0}(x)+1/2sqrtof2\phi_{1,1}(x)\\[/tex]
    [tex]<f,e_0>=\int_{0}^{1}fe_0dx[/tex]
     
    Last edited: May 17, 2010
  2. jcsd
  3. May 16, 2010 #2

    Mark44

    Staff: Mentor

    That's Fourier...
    Is there a typo above? Otherwise, why not say that f(x) = 1, 0 <= x <= 1?

    Also, I fixed your LaTeX below.
    What is the above supposed to be?
     
  4. May 17, 2010 #3
    i have changed the function
    there was a mistake
     
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