# Thread: foorier series from haar function..

1. ## foorier series from haar function..

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
?

2. i have changed the function
there was a mistake