MATLAB Help: Continous Time Frequency Selective Channel

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David83

Advanced Member level 1
Hello all,

I have the following frequency selective channel:

$h(\tau;t)=\sum_{p=0}^{N_p}h_p\delta(t-\tau_p)$

and the transmitted signal in the passband is given by:

$s(t)=\Re\left\{\sum_{k=-L}^{N-1}d_kg(t-kT_s)e^{j2 pi f_ct}\right\},\,\,\,t\in[-LT_s,NT_s]$

I want to derive the discrete time model from these equations, which should give me the traditional output:

$y_k=\sum_{l=0}^Lh_ld_{k-l}+z_k,\,\,\,k=0,1,\ldots,N-1$

where $h_l$ is the composite channel and $z_k$ is the noise both in the discrete time.

How to go through the steps in MATLAB?