All parts of this problem are concerned with the system shown in Fig. P- 12.14. In all parts of…

All parts of this problem are concerned with the system shown in Fig. P- 12.14.

In all parts of this problem, assume that X(jω) = 0 for |ω| > 1000π. In addition, assume that the C-to-D and D-to-C converters are ideal; i.e..

 

(a) Suppose that the discrete-time system is defined by y[n] = x[n]. What is the minimum value of 2π/ , such that y(t) = x(t)?

(b) Suppose that the LTI discrete-time system has system function H(z) = z -10, and assume that the sampling rate satisfies the condition of part (a). Determine the overall effective frequency response  and from it determine a general relationship between y(t) and x(t).

(c) The input/output relation for the discrete-time system is

For the value of T, chosen in part (a), the input and output Fourier transforms are related by an equation of the form Y(jω) = . Find an equation for the overall effective frequency response licejto). Plot the magnitude and phase of H,g(jw). Use MATLAB to do this or sketch it by hand.