hw9Sol - 2.6.4 Given a causal LTI system described by the dierential equation nd H(s the ROC of H(s and the impulse response h(t of the system Classify

# hw9Sol - 2.6.4 Given a causal LTI system described by the...

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2.6.4 Given acausalLTI system described by the dierential equation findH(s), the ROC ofH(s), and the impulseresponseh(t) of the system.Classify the system as stable/unstable.List the poles ofH(s).You should theMatlabresiduecommand for this problem.
2.6.6 A causal continuous-time LTI system is described by the equationy00(t) + 4y0(t) + 5y(t) =x0(t) + 2x(t)wherexis the input signal, andyis the output signal.(a) Find the impulse response of the system.(b) Accurately sketch the pole-zero diagram.(c) What is the dc gain of the system?(d) Classify the system as either stable or unstable.2.6.6) Solution 295
2.6.10 The impulse responses of eight causal continuous-time systems are illustrated below, along with the pole/zerodiagram of each system. But they are out of order. Match the figures with each other by completing the table. IMPULSE RESPONSE POLE-ZERO DIAGRAM 1 2 . . . 8 1 0 1 2 3 4 5 6 0 0.2 0.4 0.6 0.8 1 IMPULSE RESPONSE 1 1 0 1 2 3 4 5 6 0 0.2 0.4 0.6 0.8 1 IMPULSE RESPONSE 2 1 0 1 2 3 4 5 6 0 5 10 15 20 IMPULSE RESPONSE 3 1 0 1 2 3 4 5 6 0.5 0 0.5 1 IMPULSE RESPONSE 4 1 0 1 2 3 4 5 6 0.5 0 0.5 1 IMPULSE RESPONSE 5 1 0 1 2 3 4 5 6 0.5 0 0.5 1 IMPULSE RESPONSE 6 1 0 1 2 3 4 5 6 15 10 5 0 5 10 15 IMPULSE RESPONSE 7 TIME (SEC) 1 0 1 2 3 4 5 6 10 0 10 20 IMPULSE RESPONSE 8 TIME (SEC) 302
3 2 1 0 1 2 3 20 10 0 10 20 REAL IMAG POLE/ZERO DIAGRAM 6 3 2 1 0 1 2 3 20 10 0 10 20 REAL IMAG POLE/ZERO DIAGRAM 1 3 2 1 0 1 2 3 20 10 0 10 20 REAL IMAG POLE/ZERO DIAGRAM 8 3 2 1 0 1 2 3 20 10 0 10 20 REAL IMAG POLE/ZERO DIAGRAM 3 3 2 1 0 1 2 3 20 10 0 10 20 REAL IMAG POLE/ZERO DIAGRAM 2 3 2 1 0 1 2 3 20 10 0 10 20 REAL IMAG POLE/ZERO DIAGRAM 7 3 2 1 0 1 2 3 20 10 0 10 20 REAL IMAG POLE/ZERO DIAGRAM 4 3 2 1 0 1 2 3 20 10 0 10 20 REAL IMAG POLE/ZERO DIAGRAM 5 2.6.10) Solution IMPULSE RESPONSE POLE-ZERO DIAGRAM 1 6 2 1 3 8 4 3 5 2 6 7 7 4 8 5 303

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