(a) Let continuous-time signal x(t) and y(t) as shown in Fig. 2. Carefully sketch g(t) = x(t+1) + y(t-2). x(t) (5(4) Fig. 2 (b) Determine the differential equation relating the input, x(t) and the output y(t) of the system shown in Fig. 3.

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(a) Let continuous-time signal x(t) and y(t) as shown in Fig. 2. Carefully sketch
g(t) = x(t+1) + y(t-2).
x(t)
3
(5(4)
0
1-1
2
"
Fig. 2
(b) Determine the differential equation relating the input, x(t) and the output y(t) of
the system shown in Fig. 3.
Transcribed Image Text:(a) Let continuous-time signal x(t) and y(t) as shown in Fig. 2. Carefully sketch g(t) = x(t+1) + y(t-2). x(t) 3 (5(4) 0 1-1 2 " Fig. 2 (b) Determine the differential equation relating the input, x(t) and the output y(t) of the system shown in Fig. 3.
(1
+
(i)
(ii)
wi(1)
20
0.5
+
d
Win
dz
3
Fig. 3
(c) The input x (t) and output y(t) of a system is described by the following equation
dy(t)
dt
Justify whether the system is linear.
Justify whether the system is invariant.
+3ty(t) = t³x(t)
S.
Š
Transcribed Image Text:(1 + (i) (ii) wi(1) 20 0.5 + d Win dz 3 Fig. 3 (c) The input x (t) and output y(t) of a system is described by the following equation dy(t) dt Justify whether the system is linear. Justify whether the system is invariant. +3ty(t) = t³x(t) S. Š
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