Daubechies Wavelets in mulitresolutional analysis decomposition I have an understanding problem with Daubechies wavelets. 

When I use a multiresolutional analysis, I want to approximate the given input Signal $f\in L^2(\mathbb{R})$ on the subspaces $V_i$. By calculating the coefficients I split the signal in the detail part and the rest. Now I am wondering, how the Daubechies wavelet is fitting in this picture. The Daubechies wavelet is defined by coefficients, but in my opinion, these are only usable if I try to perform a wavelet decomposition on input data in $l^2(\mathbb{Z})$. 

To specify my question, I have no idea how to calculate the first inner products 
$$c_i = \langle f, \varphi_{i,j} \rangle, \text{ and } d_i = \langle f, \psi_{i,j} \rangle $$ 
if $\varphi$ and $\psi$ are Daubechies scaling function and wavelet, since they have no expression as functions in $L^2(\mathbb{R})$. 

Thanks in advance

Matthias
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.