Daubechies Wavelets in mulitresolutional analysis decomposition
As I mentioned in my comment, the reason seems to be the so-called "wavelet crime" which is taking the sampling data as the inner product. But I found a question, which is similar to mine 

Wavelet transform: How to compute the initial coefficients when only samples are available?*

This question was answered with a lot of papers, many thanks to Laurent Duval. In one of the paper 

On the Initialization of the Discrete
Wavelet Transform Algorithm  

there is a derivation to calculate the initial inner products. One can approximate the inner products as 
$$
c_k = \int_\mathbb{R} f(t)\varphi(t-k)dt \approx \varphi(-k) 
$$
And one can read the following remark: 

"A very good approximation of the time-shape of $\varphi(t)$ can
be obtained as the impulse response of the filter h convolved
with itself a large number of times. One then simply needs
to collect the samples ${\varphi(p) = \varphi(t = p)}_{p\in\mathbb{Z}}$ to perform the
approximate initialization"

Therefore it is sufficient to know the filter coefficients as given in Wikipedia.