A) Consider impulse train-sampling of a continuous-time signal x(t): x(t) = cos (2π t) + 2 cos (3π t) cos (6π t) Assume sampling rate is 5 Hz. 1) sketch the spectrum of x(t), and spectrum of the resulted weighted impulse train xp(t). 2) The frequency which, under the sampling theorem, must be exceeded by the sampling frequency is called the Nyquist rate. Find the Nyquist rate of x(t) in Hz. 3) Assume the resulted discrete-time sequence is x[n]. Sketch the DTFT of x[n].
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