a. A signal x (t) = 5 sinc2 (5πt) + cos 20πt is sampled at a rate of 10 Hz. Find the spectrum of the sampled signal. Can x (t) be reconstructed by lowpass filtering the sampled signal?
b. Repeat part (a) for a sampling frequency of 20 Hz. Can you reconstruct the signal from this sampled signal? Explain.
c. If x (t) = 5 sinc2 (5πt)+sin 20πt, can you reconstruct x (t) from the samples of x (t) at a rate of 20 Hz? Explain your answer with spectral representations(s).
d. For x (t) = 5 sinc2 (5πt) + sin 20πt, can you reconstruct x (t) from the samples of x (t) at a rate of 21 Hz? Explain your answer with spectral representation(s). Comment on your results.