How can we calculate the frequency response of each filter of a Discrete Wavelet Decomposition filter bank? 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, db7.

In reality 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 ?

Thanks

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.
The decision under the link you provided seems good enough. The main idea is:


we have impulse response of each filter
take the impulse response of the filter with the slowest sample rate as the input signal
route it back through the chain
perform spectrum estimation of the resulting signal


Division by $\sqrt2$ is for normalization only. For the given set of db coefficients their sum is $\sqrt2$, look here for explanation. It has no impact on the sense of the result I think.