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1. Consider the sinusoidal signal
x(t) = 8 sin(6Πt + φ0).
Assume φ0 = Π/4 for this question and φ0 = 0 for the following two questions. Compute analytically the spectrum. Sketch the magnitude and phase spectrum.
What is the meaning of "Nyquist rate", and what is the Nyquist rate for this signal? (Consider the signal to be a low-pass signal.)
2. The sampling function
Ts = 1/4, is used to obtain the sampled signal y(t) = x(t) • s(t).
Sketch y(t) alongside x(t) (at least 3 periods). Sketch the magnitude spectrum of y(t). Hint: Explicit computation of the spectrum Y(f) is not required.
3. Assume now Ts = 1/16. The signal x(t) is reconstructed from the sampled signal y(t) using flat-top sampling, giving the reconstructed signal z(t).
Sketch z(t) alongside x(t) (at least three periods). Discuss if the original signal x(t) can be perfectly reconstructed from z(t).
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