ng) that we not only make x(0) = 1 and x(kT - iT) = 0, but also this f(t) does not cause noise amplification. This receiver is therefore a popular choice whenever the channel is "flat" over the range of transmission frequencies. Example 9.3 Assuming a flat channel, figure out a possible g(t) and f(t) SO that there is no ISI in the received signal Vk. Solution: Equation (9.24) shows us the received Vk when the channel is flat. If we want to get rid of ISI (the middle term), all we have to do is make sure that x(t) = g(t) * h (t) satisfies Equation (9.25). The easiest way to find a g(t) and h(t) that satisfy Equation (9.25), the easiest way is to find an x(t) = g(t) * h(t) that satisfies (E9.15) To solve for the g(t) and h(t) from here, turn to the frequency domain, where we find out that we can write Equation (9.25) according to (E9.16) 0, else Chapter Nine One solution to this equation is to let (E9.17) Turning this back to the time domain we end up with (E9.18) So, here is one possible g(t) and h(t) that satisfies Equation (9.25), insuring that in a flat channel we get no ISI. 9.4 Optimal Receiver Front End So far, we considered one example of a possible receiver, shown in Figure 9.6. This receiver explains the idea of a receiver filter f(t) and how it can be used to remove intersymbol interference (ISI). In the case where the channel is "flat" over the frequen- cies of transmission, that receiver actually turns out to be the optimal receiver. But in other cases, that receiver causes noise amplification, and may not be a very good one. You need alternatives! You need choices! You'll want to know how to build the very best receiver possible. That's why this section is here-to tell you exactly how to build the optimal receiver front end, which is the first part of the optimal receiver. We start at our receiver with the input (9.26) where a(t)=g(t)*cg(t). Without any loss of information, we can map this r(t) signal to a signal without the carrier ejwet We do this by multiplying the r(t) by a cosine and then by a si