Consider the signal xct sin2 pi40t How fast must xct be sam

Consider the signal x_c(t) = sin(2 pi(40)t). How fast must x_c(t) be sampled to avoid aliasing? Determine the Nyquist rate (the frequency which the sampling rate f_s must exceed) for x_c(t). Consider processing the signal x_c(t) (from part using the system shown below: The sampling period for this system is T = 1/50 seconds. The DT system H(e^j ohm) is an ideal lowpass filter with gain 1 and cutoff omega_c = pi/2. Plot for two periods. Fully label your plot. Determine and sketch the Fourier transforms (some are CTFTs and some are DTFTs -pay attention!) of x_c (t), x_p(t), x[n], y[n], y_p(t), and y_c(t). Fully label your sketches. What is the output signal y_c(t)? Write an analytical expression for it. Explain (in one or two sentences), the concept of aliasing. Does aliasing occur when x_c(t) is sampled as described above?

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