1 12 IMPULSE RESPONSE 3 10 20 30 40 5 10 15 20 25 IMPULSE RESPONSE 6 10 20 30

1 12 impulse response 3 10 20 30 40 5 10 15 20 25

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1 1.2 IMPULSE RESPONSE 3 0 10 20 30 40 0 5 10 15 20 25 IMPULSE RESPONSE 6 0 10 20 30 40 - 1 - 0.5 0 0.5 1 IMPULSE RESPONSE 5 0 10 20 30 40 - 20 - 10 0 10 20 IMPULSE RESPONSE 1 1.7.9) Solution 115
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POLE-ZERO DIAGRAM IMPULSE RESPONSE 1 5 2 7 3 4 4 6 5 1 6 3 7 8 8 2 116
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1.7.10 The impulse response of a discrete-time LTI system is given byh(n) =A(0.7)nu(n).Suppose the signalx(n) =B(0.9)nu(n)is input to the system.AandBare unknown constants. Which of the following could be the output signaly(n)?Choose all that apply and provide an explanation for your answer. (a)y(n) =K1(1.6)nu(n) +K2(0.2)nu(n)(b)y(n) =K1(0.7)nu(-n) +K2(0.2)nu(-n)(c)y(n) =K1(0.7)nu(n) +K2(0.9)nu(n)(d)y(n) =K1(0.7)nu(n) +K2(0.2)nu(-n)(e)y(n) =K1(0.7)nu(n) +K2(0.2)nu(n) +K3(0.9)nu(n)(f)y(n) =K1(0.7)nu(n) +K2(0.2)nu(n) +K3u(n)1.7.10)SolutionOnly (c). Consider thatY(z) =H(z)X(z) will have a second order denominator. After partial fraction expansionand conversion toy(n) the output signal (c) is the only possible form. 117
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1.7.11 The impulse response of a discrete-time LTI system is given byh(n) =A(0.7)nu(n).Suppose the signalx(n) =Bcos(0.2n)u(n)is input to the system.AandBare unknown constants. Which of the following could be the output signaly(n)?Choose all that apply and provide an explanation for your answer. 118
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