2.9. The signals in Figs. 2-14(a) and (b) are the input x(t) and the output y(t), respectively, of a certain continuous-time LTI system. Sketch the output to the following inputs: (a) x(t – 2); (b) , x(1). (a) Since the system is time-invariant, the output will be y(t – 2), which is sketched in Fig. 2-14(c). (b) Since the system is linear, the output will be y(1), which is sketched in Fig. 2-14(d). x(t) y(t) 2 1 1 -1 0 1 -1 1 3 (a) (b) y(t-2) 1 1 -1 1 4 -1 0 1 3 (c) (d) Fig. 2-14 1/2 2. 2.

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Properties of Continuous-Time LTI Systems
2.9. The signals in Figs. 2-14(a) and (b) are the input x(t) and the output y(t), respectively, of a certain
continuous-time LTI system. Sketch the output to the following inputs: (a) x(t – 2); (b) x(1).
(a) Since the system is time-invariant, the output will be y(t - 2), which is sketched in Fig. 2-14(c).
(b) Since the system is linear, the output will be y(1), which is sketched in Fig. 2-14(d).
x(t)
y(t)
2
1
1
-1
1
-1
1
3
(а)
(b)
y(t-2)
2
1
1
-1 0 1
3
-1 0 1
(c)
(d)
Fig. 2-14
Transcribed Image Text:Properties of Continuous-Time LTI Systems 2.9. The signals in Figs. 2-14(a) and (b) are the input x(t) and the output y(t), respectively, of a certain continuous-time LTI system. Sketch the output to the following inputs: (a) x(t – 2); (b) x(1). (a) Since the system is time-invariant, the output will be y(t - 2), which is sketched in Fig. 2-14(c). (b) Since the system is linear, the output will be y(1), which is sketched in Fig. 2-14(d). x(t) y(t) 2 1 1 -1 1 -1 1 3 (а) (b) y(t-2) 2 1 1 -1 0 1 3 -1 0 1 (c) (d) Fig. 2-14
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