1
vote
1answer
53 views

Integrating a squared Haar wavelet function

I'm studying about wavelets and here is one derivation I couldn't understand: The constant that makes this orthogonal basis orthonormal is $2^{j/2}$. Indeed, from the definition of norm$^2$ in ...
3
votes
3answers
96 views

Orthogonality of Haar wavelet functions

I'm reading about wavelets and I bumped into the follwing: $\text{Haar wavelet is a step function}\; \psi(x), \text{which takes values 1 and -1, when}\; x \;\text{is in the ranges}\; [0, \frac{1}{2}) ...
4
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1answer
163 views

Question in solving $\phi(t)=\phi(2t)+\phi(2t-1)$, $\phi\ne0$

Actually one can resort to the two-scale equation in multiresolution analysis. Perform Fourier transformation on both side of $\phi(t)=\phi(2t)+\phi(2t-1)$, it turns out that ...