9. a) A signal x(t) is given in Figure 9.a. Represent the signals x1(t), x:(t) and x:(t); using x(t) only. x(t) + x (t) Xa(t) 2 + x(t) 1 0.5 -1 -2 -1 -1 Figure 9.a 9. b) Consider the LTI systems whose impulse responses are (i) h, (1) = u(21) – u(t – 2) (ii) h, (1) = 8(1 - 3) + 3e [u(t) – u(t - 4)1 (iii) h, (1) = te "u(1)+8(1 –1)+[u(1 – 2)- u(t- 3)] Determine whether the systems are causal/noncausal, with/without memory and stable/unstable.

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9. a) A signal x(t) is given in Figure 9.a. Represent the signals x (t), x2(t) and xa(t); using x(t) only.
x(t)
+ x (t)
Xa(t)
2
+ x:(t)
1
0.5
-1
1
-1
2
Figure 9.a
9. b) Consider the LTI systems whose impulse responses are
(i) h, (1) = u(21) – u(t – 2)
(ii) h, (1) = 8(1 - 3) + 3e[u(t) – u(t - 4)1
(iii) h,(1) = te "u(t)+ 8(1–1) +[u(t – 2)-u(t-3)]
Determine whether the systems are causal/noncausal, with/without memory and stable/unstable.
Transcribed Image Text:9. a) A signal x(t) is given in Figure 9.a. Represent the signals x (t), x2(t) and xa(t); using x(t) only. x(t) + x (t) Xa(t) 2 + x:(t) 1 0.5 -1 1 -1 2 Figure 9.a 9. b) Consider the LTI systems whose impulse responses are (i) h, (1) = u(21) – u(t – 2) (ii) h, (1) = 8(1 - 3) + 3e[u(t) – u(t - 4)1 (iii) h,(1) = te "u(t)+ 8(1–1) +[u(t – 2)-u(t-3)] Determine whether the systems are causal/noncausal, with/without memory and stable/unstable.
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