Answer Happy

(b) (8 marks) Consider a system first sampling 22(t) = 1+{cos(3000mt)+sin(4000+t) by a impulse train p(t) = -x 8(t - nT), and then using a filter with spectrum H(w) to reconstruct it, as illustrated in Fig. 2. i) (3 marks) Suppose this system uses sampling at T = 4000 s. Express the spectrum for the sampled signal Xp(t), \Xp(w)], in terms of X2(W)], and sketch |Xp(w). ii) (5 marks) Now, suppose this system uses an advanced sampling and reconstructing tech- nique. It sets T = 2000 s for sampling and uses a band-pass filter to reconstruct. The spectrum of this band-pass filter is given in Fig. 3. The spectrum of the reconstructed signal r(t) is given by X-(w) = cx |H(w) x Xp(w), where c is a constant. Under this setting, sketch the spectrum |X(w) for the sampled signal 2-p(t), and specify the range of wa (see Fig. 3) such that Ir(t) is a perfect reconstruction. | H(0) -a 4 m = 0), + 1050x Figure 3: The spectrum |H(jw) in Question (b)-ii), Problem 5.