I am getting started with wavelets! And I am having trouble going from scaling function to the frequency response of the scaling function.
The scaling function and wavelet is defined on some axis (say $x$). Say for instance we are considering $\phi(x)$. Now this is defined on $x$ axis, and my target function is also defined on $x$ axis. What we do is take the projection of function on the basis functions to get the coefficients. Same is the case for wavelets.
The trouble I am facing is where exactly frequency kicks in. I undertand wavelets are high-pass filter, because they allow to jump from coarser scale to finer scale, hence they need to pull in high frequencies. But I do not understand how exactly get the frequency responses of these functions.
Do I have to use DFT for the frequency content of the functions?
Appreciate your help!