I am using the Multilevel Wavelet decomposition. The decomposition results in a filter bank such as the following:
Specifically, I am using one of the Daubechies wavelets,
Level 2 coefficients are the result of filtering by $\ g(n)$ then down-sampling and filtering by $\ h(n)$. Suppose that the whole operation I described above is a single filter ie. at each level the coefficients get generated by a single filter.
I would like to know how to calculate the frequency response of those filters at each level.
Is it correct to feed an impulse, i.e a Kronecker Delta function to the wavelet decomposition and then compute the Fourier Transform of the resulting coefficients ?
PS: The same question has been asked here and the response was to get the
convolution of the impulse response of $\ g(n)$ and an up-sampled version of $\ h(n)$. What puzzles me in that response though, is why divide by $\sqrt2$ the result of the convolution. Also, it seems like more code compared to just calling the wavelet decomposition routine with a Kronecker delta function.