Question

A signal x(t) has frequency spectra shown below Xl) 100 -100 a) At what minimum frequency should x(t) be sampled so that no aliasing occurs b) If x(t) is sampled at 150 rad/sec, sketch the frequency spectra of the sampled signal Consider the feedback system shown below. y(t) x(t) H3 (s) Show that the overall transfer function of the system is given by a) H(s)H(s) 1+H1(S) (10 points) = b) If Hi (s) ,and x(t) 3e3 u(t), find the output y(t) s+1

Can I get this two questions's solution, please correct solutions will be given thumb up

Answer 1

Given Frequency spectra minimum frequency should x(t) be sampled so that no aliasing occurs is Nyquist frequency Nyquist Frequency rightarrow sampling at exact double the x(t) frequency i.e., omega_sampling = 2 omega_m = > Nyquist frequency = 2 times 100 r/s = 200 rad/sec when x(t) is sampled at 150 rad/sec, Aliasing must occurs. E(s) = x(s) - y(s) y(s) = E(s)[H_1(s)] = > y(s) = H_1(s) [times (s) - y(s)] + > Y(s) [1 + H_1(s)] = H_1(s) times (s) = > y(s)/x(s) = h_1(s)/1 + H_1(s) H_1(s) = 1/s + 1 and x(t) = 3 e^-3t 4(t): y (t) = ? x(t) = 3 e^-3t 4(t) doubleheadarrow x(s) = 3/s + 3 [Because E^-at u(t) doubleheadarrow 1/s + a] = > t(s) = x(s) H_1(s)/1 + H_1(s) = (3/s + 3) 1/s + 1/1 + 1/c + 1 = (3/s + 3)/s + 1 + 1 = (3/s + 3)/s + 2 = > y(s) = 3/(s + 3)(s + 2) = A/s + 3 + B/s + 2 A = y(s) (s + 3)/ s = -3 = 3/s + 2/s = -3 = 3/-1 = -3