The impulse response of a channel used for PAM communication is specified by h(t) =

Chapter 8, Problem 8.43

(choose chapter or problem)

The impulse response of a channel used for PAM communication is specified by h(t) = 10,000e-I,OOOtu(t). It is assumed that the phase response of the channel is approximately linear in the bandwidth of the channel. A pulse that is received after passing through the channel is processed using an LTI systemS with impulse response g(t) in order to compensate for the nonuniform gain over the channel bandwidth. (a) Verify that if g(t) has the Fourier transform G(jw) = A+ }Bw, where A and Bare real constants, then g(t) can compensate for the nonuniform gain over the channel bandwidth. Determine the values of A and B. (b) It is proposed that S be implemented with the system shown in Figure P8.43. Determine the values of the gain factors a and f3 in this system. x(t) (Received signal before compensation) x(t) Figure P8.43 y(t) (Received signal after compensation)