A) Consider impulse train-sampling of a continuous-time signal x(t): x(t) = cos (2nt) + 2 cos (3nt) cos (6nt) Assume sampling rate is 5 Hz. 1) sketch the spectrum of x(t), and spectrum of the resulted weighted impulse train xp (t). 2) The frequency which, under the sampling theorem, must be exceeded by the sampling frequency is called the Nyquist rate. Find the Nyquist rate of x(t) in Hz. 3) Assume the resulted discrete-time sequence is x[n]. Sketch the DTFT of x[n]. B) Consider the system in Figure 1.1. x(t) is sampled with a periodic impulse train, and a reconstructed signal x, (t) is obtained from the samples by lowpass filtering. The sampling period T = 1 ms, and x(t) is a sinusoidal signal of the form x(t) = cos (2nfot + 0). x(t) X xp (1) p(t) = (t - nT) n=100 T H(2) FIL Figure 1.1 For each of the following choices of fo and 0, determine x,. (t). 1) fo = 250 Hz, 0 = /4 2) fo 750 Hz, 0 = /2 = x, (t)