Consider the representation of the process of sampling followed by reconstruction shown in Figure below s(t)...

 

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Consider the representation of the process of sampling followed by reconstruction shown in Figure below s(t) = Σ 8(t-nT) 8(t-n7) x-(1) x x(1) Assume that the input signal is H,(jQ2) xc(t) = 2 cos(100лt-/4)+cos(300лt+л/3) -∞<t<∞ The frequency response of the reconstruction filter is x-(1) T |22| ≤ T/T |22|>1/T H,(j) = 0 (a) Determine the continuous-time Fourier transform Xe(j2) and plot it as a function of S2. (b) Assume that fs = 1/T = 500 samples/sec and plot the Fourier transform X, (j) as a function of 2 for -2л/T ≤ ≤2/T. What is the output x, (t) in this case? (You should be able to give an exact equation for xr(t).) (c) Now, assume that fs = 1/T = 250 samples/sec. Repeat part (b) for this condition. (d) Is it possible to choose the sampling rate so that xr (t) = A + 2 cos(100лt - π/4) where A is a constant? If so, what is the sampling rate fs numerical value of A? = 1/T, and what is the Consider the representation of the process of sampling followed by reconstruction shown in Figure below s(t) = Σ 8(t-nT) 8(t-n7) x-(1) x x(1) Assume that the input signal is H,(jQ2) xc(t) = 2 cos(100лt-/4)+cos(300лt+л/3) -∞<t<∞ The frequency response of the reconstruction filter is x-(1) T |22| ≤ T/T |22|>1/T H,(j) = 0 (a) Determine the continuous-time Fourier transform Xe(j2) and plot it as a function of S2. (b) Assume that fs = 1/T = 500 samples/sec and plot the Fourier transform X, (j) as a function of 2 for -2л/T ≤ ≤2/T. What is the output x, (t) in this case? (You should be able to give an exact equation for xr(t).) (c) Now, assume that fs = 1/T = 250 samples/sec. Repeat part (b) for this condition. (d) Is it possible to choose the sampling rate so that xr (t) = A + 2 cos(100лt - π/4) where A is a constant? If so, what is the sampling rate fs numerical value of A? = 1/T, and what is the

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