## Understanding Sampling

Hello all,

I am trying to understand sampling from the following:

Suppose the channel impulse response is given by:

$3h(\tau)=h\delta(\tau)$

and the transmitted signal is:

$3s(t)=\sum_ks_kg(t-kT_s)$

where {s_k} are the transmitted symbols and g(t) is a rectangular pulse of duratuion Ts the sample time. The received signal can by written as:

$3v(t)=h\sum_ks_kg(t-kT_s)+w(t)$

where w(t) is the additive noise. We can sample the above received signal at t=nTs resulting in:

$3v_n=hs_n+w_n$ .... (1)

which is obvious. Now suppose I want to take another approach, say to find the optimum receiver from the received signal v(t) as:

$3v_n=h^*\int_{-\infty}^{\infty}v(t)g(t-nT_s)\,dt=h^*\int_{nT_s}^{(n+1)T_s}v(t)\,dt$ .... (2)

which must be the same as multiplying (1) by conj(h). Does this mean that the integration in (2) is effectively sampling, which means that:

$3\int_{nT_s}^{(n+1)T_s}v(t)\,dt=v(nT_s)$??