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QUESTION 2 (20 MARKS) (a) A continuous time signal x(t) = 3e2tu(-t) is an input to...


QUESTION 2 (20 MARKS) (a) A continuous time signal x(t) = 3e2tu(-t) is an input to a Linear Time Invariant system of which th
QUESTION 2 (20 MARKS) (a) A continuous time signal x(t) = 3e2tu(-t) is an input to a Linear Time Invariant system of which the impulse response h(t) is shown as h(t) = { .. 12, -osts-2 elsewhere Compute the output y(t) of the system above using convolution in time domain for all values of time t. [8 marks) (b) The impulse response h[n] of an LTI system is given as a[n] = 4(0.6)”u[n] Determine if the system is stable. [3 marks) (c) Given a causal LTI system described by y[n] – vln – 1] + X «In – 2] = 2x[n – 1] Determine the impulse response h[n] of this system. You are NOT ALLOWED to use any transform methods (assume initial rest). [9 marks)
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لن Given 2+ 201+ = 3€ (-+) and hit) 2 -oots-2 - 244-2 otherwise he Knowe that output recill be g(t) = htact) - Se h(t) alt-t(2) 6) Given Impulse Response of ahhts system is n h {n} = 4/006 ulo) condition for stability :- If impulse response is absolso system is stable © y[n] - 4 + 3_ y[n-2) = 2X[ns] -0 2 We then 2 know that that if if a[n] = {[n] output of y (n] = b[n] Imto. [n] - [n] 3 hn-21 +28Cn-17 20 for M=0, 10JE 오 네 3 V-2) +28-1 =0+O4O 5 hj= for, n= J E 도시이 3 HJ+ 2810) - 20 오x0.3 kp + 2xl

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