20102ee113_1_homework5

20102ee113_1_homework5 - EE113 Digital Signal Processing...

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Some of the following problems are from the electronic versions of the chapters of An Undergraduate Course on Discrete-Time Signal Processing , by Prof. A.H. Sayed (posted on the class website): Problem 10.2, 11.2, 11.9 In addition: Problem C. A causal LTI system has impulse response () hn , for which the z -transform is. 1 11 1 24 z Hz zz - -- + = æö ÷÷ çç -+ èø . (a) What is the region of convergence of ? (b) Is the system stable? Explain. (c) Find the z -transform Xz of an input ( ) xn that will produce the output 4 21 34 3 n n yn un u n ÷ ç =- - - - - ÷ ç ÷ ç . (d) Find the impulse response of the system. Problem D. Consider an LTI system with input and output that satisfies the difference equation 5 12 1 2 xn xn + - = - - . Determine all possible values for the system’s impulse response
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20102ee113_1_homework5 - EE113 Digital Signal Processing...

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