Question

Consider the sampling and reconstruction configuration in Fig. (a), below. The outputy() of the ideal reconstruction can be found by sending the sampled signal xp(1) = x(1)p(1)through an ideal low-pass filter with frequency response H(jo) in Fig. (b), \text { where: } p(t)=\sum_{n=-\infty}^{\infty} \delta(t-n T) \text {. Given the input signal } x(t)=1+\cos (40 \pi t) \text { and the } sampling period 7 = 0.025 sec. (i) Determine and sketch Xp(jo) (the spectrum of xp(1)), clearly labeled and showingall values of magnitude and corresponding frequency. (ii) Sketch Y(jo), clearly labeled and showing all values of magnitude and corresponding frequency. (iii) Determine the expression for y() and state, with justification, if aliasing occurs. (iv) Determine the expression for x[n].

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