The input to the C-to-D converter in Fig. P-6.15 is (a) Suppose that the impulse response...

The input to the C-to-D converter in Fig. P-6.15 is

(a) Suppose that the impulse response of the LTI system is h[n] = δ[n]. If ω0 = 2π (500), for what values of fs = 1/Ts, is it true that y(t) = x(t)?

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(b) Now suppose that the impulse response of the LTI system is changed to h[n] = δ[n − 10]. Determine the sampling rate fs = 1/Ts and a range of values for ω0 so that the output of the overall system is

 

for −∞ < t < ∞.

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(c) Suppose that the LTI system is a 5-point moving averager whose frequency response is

 

If the sampling rate is fs = 2000 samples/sec, determine all values of ω0 such that the output is equal to a constant (i.e., y(t) = A for −∞ < t < ∞). Also, determine the constant A in this case.