A simple model of a multipath communication channel is indicated inFigure P4.7-1. Assume...

A simple model of a multipath communication channel is indicated inFigure P4.7-1. Assume

that s_c(t) is bandlimited such that and that xc(t) is sampled with

a sampling period T to obtain the sequence

(a) Determine the Fourier transform of xc(t) and the Fourier transform of x[n] in terms of S_c(jΩ).

(b) We want to simulate the multipath system with a discrete-time system by choosing H(ejω) in Figure P4.7-2 so that the output r[n] = x_c(nT ) when the input is s[n] = s_c(nT ). Determine H(e^jω) in terms of T and t_d .

(c) Determine the impulse response h[n] in Figure P4.7 when (i) τd = T and (ii) τd = T/2.