Consider the signal x(t) = cos(20πt) + 5sinc 0 (5t). (a) Determine and sketch the spectrum X(ω) of signal x(t) when sampled at a rate of 10 Hz. Can x(t) be reconstructed by lowpass filtering the...

Consider the signal x(t) = cos(20πt) + 5sinc⁰(5t).

(a) Determine and sketch the spectrum X(ω) of signal x(t) when sampled at a rate of 10 Hz. Can x(t) be reconstructed by lowpass filtering the sampled signal? Explain.

(b) Repeat part (a) for the sampling frequency F_s
= 20 Hz.