3. (a) Consider the signal xc(t)-sin(2π(40)t). How fast must xe(t) be sanpled to avoid aliasing? Determine the Nyquist rate (the frequency which the sampling rate fs must exceed) for ae(t) (b) Consider processing the signal xe(t) (from part (a)) using the system shown below: Conversion to a sequence Conversion to an impulse train Ideal Reconstruction Filter Hr(ju) p (t) ур y(t) The sampling period for this system is T-1/50 seconds. The DT system H(ei2) is an ideal lowpass filter with gain 1 and cutoff wc T/2. i. Plot He?9) for two periods. Fully label your plot. ii. Determine and sketch the Fourier transforms (some are CTFTs and some are DTFTs pay attention!) of rc(t), xp(t), rn], y[n], yp(t), and y(t). Fully label your sketches iii. What is the output signal ye(t)? Write an analytical expression for it 3. (a) Consider the signal xc(t)-sin(2π(40)t). How fast must xe(t) be sanpled to avoid aliasing? Determine the Nyquist rate (the frequency which the sampling rate fs must exceed) for ae(t) (b) Consider processing the signal xe(t) (from part (a)) using the system shown below: Conversion to a sequence Conversion to an impulse train Ideal Reconstruction Filter Hr(ju) p (t) ур y(t) The sampling period for this system is T-1/50 seconds. The DT system H(ei2) is an ideal lowpass filter with gain 1 and cutoff wc T/2. i. Plot He?9) for two periods. Fully label your plot. ii. Determine and sketch the Fourier transforms (some are CTFTs and some are DTFTs pay attention!) of rc(t), xp(t), rn], y[n], yp(t), and y(t). Fully label your sketches iii. What is the output signal ye(t)? Write an analytical expression for it