5.1 Pulse amplitude modulation through bandlimited channel

Consider a PAM system $b_{-10}$ ,, $b_{-1}$ , $b_0$ $b_1$ ,

This implies

The received signal is

Since the signals span a one-dimensional space, one filter matched to $\stackrel{}{s}(t)=\overline{s}g(t)$ is sufficient.

The matched filter's impulse response is

The decision on the $k^{\mathrm{th}}$ symbol is obtained by sampling the MF output at $kT$ :

Since the channel is bandlimited, it provides memory for the transmission system. The effect of old symbols (possibly evenfuture signals) lingers and affects the performance of the receiver. The effect of ISI can be eliminated or controlled byproper design of modulation signals or precoding filters at the transmitter, or by equalizers or sequence detectors at the receiver.