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(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n) as shown in Figure 1, where K 6 (conssystem #1 system #2 yin) x(n) K Figure 1: The block diagram of the composite system: Problem 2. (c) Deri the overall frequenc

(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n) as shown in Figure 1, where K 6 (constant), system #1 is described by its impulse response: h(n) = -36(n) + 0.48(n- 1)+8.26(n-2), and system # 2 has the difference equation given by: y(n)+0.1y(n-1)+0.3y(n-2)- 2a(n). (a) Determine the corresponding difference equation of the system #1. Hence, write its fre- quency response. (b) Find the frequency response of system #2. 1
system #1 system #2 yin) x(n) K Figure 1: The block diagram of the composite system: Problem 2. (c) Deri the overall frequency response H(e), and the corresponding difference equation. (d) Plot the magnitude and phase responses. What is the kind of the filter? (e) Consider the signal r(n) = sin(/2n + /3). Write an expression of the corresponding steady state output. 2
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