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.