Foorier series from haar function

1. May 16, 2010

nhrock3

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:
$$L_0=\phi_{0,-1}(x)=1\\$$
$$L_1=\phi_{0,0}(x)=\begin{Bmatrix}1,0\leq x\leq 0.5 \\ -1,-0.5\leq x\leq 1 end{Bmatrix}\\$$
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}\\
$$aL_0+bL_1\\$$
$$L_2=\phi{0,1}(x)\\$$
$$L_3=\phi{1,1}(x)\\$$
$$f=0.75\phi_{0,-1}(x)+1/4\phi_{0,0}(x)+1/2sqrtof2\phi_{1,1}(x)\\$$
$$<f,e_0>=\int_{0}^{1}fe_0dx$$

Last edited: May 17, 2010
2. May 16, 2010

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?

3. May 17, 2010

nhrock3

i have changed the function
there was a mistake