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 $2^{j/2}\psi (2^{j}x-k)$. What are the significant properties of the dual wavelet? --Cebus (talk) 21:35, 14 December 2016 (UTC)