Talk:Dual wavelet

Whats the difference between

$$ \psi_{jk} = \psi^{jk} $$

???
 * $$\psi_{jk}$$ and $$\psi^{jk}$$ are different functions, which are related by orthogonality relation $$\langle \psi^{jk} \vert \psi_{lm} \rangle = \delta_{jl} \delta_{km}$$. --Cebus (talk) 21:29, 14 December 2016 (UTC)

Properties, motivation?
The article gives a definition of the dual wavelet, but there is no motivation for the somewhat peculiar ansatz $$2^{j/2}\psi(2^jx-k)$$. What are the significant properties of the dual wavelet? --Cebus (talk) 21:35, 14 December 2016 (UTC)