Q4.- A signal x(t) = 3 cos(6000xt) + cos(15000) is sampled at a rate of 9000 samples/sec. The sampling process is modeled by the system shown below. Xp(t) x(t) (x) p(t) = 8(t-kTs) k=-o (a) Sketch the spectrum of the sampled signal Xp(t) in the range -13... 13 kHz. (b) Can the original signal x(t) be recovered from Xp(t) by using a low-pass reconstruction filter? Justify. (c) If your answer to part (b) is 'yes', explain how x(t) can be recovered and provide the values of the parameters, gain & cutoff frequency oc, needed to do this. If your answer to part (b) is 'no', propose how you could modify the sampling train of impulses such that x(t) can be recovered from Xp(t). (d) Describe how the sampling system shown above can be modified such that using a sampling rate of 9000 samples/second the 3 cos(6000t) part of the signal can still be faithfully represented in the discrete-time domain without distortion. [5 pts] [3 pts] [3 pts] [5 pts]