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Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition 9 53 Copyright © Orchard Publications Exercises 9.10 Exercises 1 . Find the Z transform of the discrete time pulse defined as 2 . Find the Z transform of where is defined as in Exercise 1. 3 . Prove the following Z transform pairs: a. b. c. d. e. 4 . Use the partial fraction expansion to find given that 5 . Use the partial fraction expansion method to compute the Inverse Z transform of 6 . Use the Inversion Integral to compute the Inverse Z transform of 7 . Use the long division method to compute the first 5 terms of the discrete time sequence whose Z transform is 8 . a. Compute the transfer function of the difference equation b. Compute the response when the input is pn [] 1 n 0 1 2 m1 ,,, , = 0 otherwise = a n δ n 1 ⇔δ n1 z m na n u 0 n az za () 2 ------------------ n 2 a n u 0 n az z a + 3 ---------------------- + u 0 n z 2 z1 2 fn Z 1 Fz = A 1z 1 10 . 5 z 1 -------------------------------------------------- = z 2 + z0 . 7 5 2 ------------------------------------------- = 12 z 1 z 3 ++ 1 . 5 z 1 = z 1 z 2 z 3 + 1 z 2 4z 3 +++ ----------------------------------------------- = yn yn 1 Tx n 1 = xn e naT =

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Chapter 9 Discrete Time Systems and the Z Transform 9 54 Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition Copyright © Orchard Publications 9 . Given the difference equation a. Compute the discrete transfer function b. Compute the response to the input 10 .A d i sc re te time system is described by the difference equation where a. Compute the transfer function b. Compute the impulse response c. Compute the response when the input is 11 . Given the discrete transfer function write the difference equation that relates the output to the input . yn [] yn 1 T 2 --- xn xn 1 + {} = Hz () xn e naT = + = 0 for n 0 < = hn 10 n 0 = z2 + 8z 2 2z 3 ---------------------------- =
Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition 9 55 Copyright © Orchard Publications Solutions to End of Chapter Exercises 9.11 Solutions to End of Chapter Exercises 1 .

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