http://mathworld.wolfram.com/HaarFunction.html

$\displaystyle f(x)= {1, 0<=x<3/4}$

$\displaystyle f(x)= {1, 3/4<=x<=1}$

calculate the foorier function with haar group

here is the solution:

$\displaystyle L_0=\phi_{0,-1}(x)=1\\$

$\displaystyle 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

e_1=\phi_{0,0}(x)=\begin{Bmatrix}1,0\leq x\leq 0.5

\\

-1,-0.5\leq x\leq 1

end{Bmatrix}\\

$\displaystyle aL_0+bL_1\\$

$\displaystyle e_2=\phi{0,1}(x)\\$

$\displaystyle e_3=\phi{1,1}(x)\\$

$\displaystyle f=0.75\phi_{0,-1}(x)+1/4\phi_{0,0}(x)+1/2sqrtof2\phi_{1,1}(x)\\$

$\displaystyle <f,e_0>=\int_{0}^{1}fe_0dx$

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

?