Harr Wavelet Question: Proving Orthogonality of Psi_2,1 and Psi_2,0

[ChickysPusss]

Homework Statement

I think this may be a simple problem, but I really have no idea if I did it right because it seemed to easy.

Here's the question, consider the Harr Wavelet $\psi$$^{}_n{}$$_,{}$$_k{}$(x) = 2$^n{}$$^/{}$$^2{}$*$\psi$(2$^n{}$x-k) where $\psi$ is the mother wavelet.

Prove that $\psi$$^{}_2{}$$_,{}$$_1{}$ and $\psi$$^{}_2{}$$_,{}$$_0{}$ are orthogonal.

2. Homework Equations

The mother wavelet of a Harr wavelet is a piecewise function that says

$\psi$(x) = 1 if 0<=t<1/2
-1 if 1/2 <= t <= 1
0 otherwise

The Attempt at a Solution

I plugged in the n and k values that we are meant to prove, and found that we get
$\psi$(4x-1) and $\psi$(4x)

Graphing these functions show that they are both clearly integrated to zero, so is this proof that they are orthogonal?

 

[voko]

Two functions are orthogonal when their product integrates to zero.