- #1
ChickysPusss
- 13
- 1
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 [itex]\psi[/itex][itex]^{}_n{}[/itex][itex]_,{}[/itex][itex]_k{}[/itex](x) = 2[itex]^n{}[/itex][itex]^/{}[/itex][itex]^2{}[/itex]*[itex]\psi[/itex](2[itex]^n{}[/itex]x-k) where [itex]\psi[/itex] is the mother wavelet.
Prove that [itex]\psi[/itex][itex]^{}_2{}[/itex][itex]_,{}[/itex][itex]_1{}[/itex] and [itex]\psi[/itex][itex]^{}_2{}[/itex][itex]_,{}[/itex][itex]_0{}[/itex] are orthogonal.
2. Homework Equations
The mother wavelet of a Harr wavelet is a piecewise function that says
[itex]\psi[/itex](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
[itex]\psi[/itex](4x-1) and [itex]\psi[/itex](4x)
Graphing these functions show that they are both clearly integrated to zero, so is this proof that they are orthogonal?