Consider the system in Figure 4.10. The input signal xc(t) has the Fourier transform sho...

Consider the system in Figure 4.10. The input signal x_c(t) has the Fourier transform shown in Figure P4.20 with Ω₀ = 2π(1000) radians/second. The discrete-time system is an ideal lowpass filter with frequency response

(a) What is the minimum sampling rate F_s = 1/T such that no aliasing occurs in sampling the input?

(b) If ω_c = π/2, what is the minimum sampling rate such that y_r (t) = x_c(t)?