A simple model of a multipath communication channel is indicated in Figure. Assume that s_c(t) is band limited such that S_c(j?) = 0 for |?| ? ? / T and that x_c(t) is sampled with a sampling period T to obtain the sequence

x[n] = x_c(nT).

(a) Determine the Fourier transform of x_c(t) and the Fourier transform of x[n] in terms of S_c(j?).

(b) We want to simulate the multipath system with a discrete-time system by choosing H(e^j?) in Figure so that the output r[n] = x_c(nT) when the input is s[n] = s_c(nT). Determine H(e^j?) in terms of T and t_d

(c) Determine the impulse response h[n] in Figure, when (i) t_d = T and (ii) t_d = T/2.

Transcribed Image Text:

$ (1) x,(1) = s,(1) + a s, (1- Ta) Delay Part C H(e) rIn)=x,(nT) s[n] = s,(nT)