All parts of this problem are concerned with the system shown in Fig. P-12.1Figure p-12.1I...

All parts of this problem are concerned with the system shown in Fig. P-12.1

Figure p-12.1

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/Ts 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 Heff(jω) 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 Ts chosen in part (a), the input and output Fourier transforms are related by an equation of the form Y(jω)= Heff(jω)X(jω). Find an equation for the overall effective frequency response Heff(jω). Plot the magnitude and phase of Heff(jω). Use Matlab to do this or sketch it by hand.