I am studying wavelets and somenthing that catch my attention is the existance of a so caled scaling function $\Phi$. Let's take the Haar wavelet. I do not understand why is the scalling function different from the wavelet itself, after all they are both needed for a base right? I really want to understand why is there and why is different to the wavelet.
So far what I have noticed is that the $\Phi$ function is always the low-pass filter, but still do not get the name and the implicance.
Thank you all in advance!