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Homework_6 - 1 EE113 Homework 6 Problem 8.37 The input...

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Unformatted text preview: 1 EE113 Homework 6 Problem 8.37 The input sequence x ( n ) = u ( n- 1) is first processed by the causal system y ( n ) = 2 y ( n- 1) + x ( n ) , y (- 1) = 1 The result, y ( n ) , is then processed by an LTI system with impulse response sequence h ( n ) = { 1 ,- 1 } What is the output of this second system? Problem 8.41 Find the complete response of the causal system y ( n )- 2 3 y ( n- 1)- 1 3 y ( n- 2) = x ( n ) , y (- 2) = 1 , y (- 1) = 0 to the input sequence x ( n ) = 1 2 u ( n- 2) + parenleftbigg 1 4 parenrightbigg n- 1 u ( n ) Check your answer. Problem 8.45 Consider the difference equation y ( n ) = 5 2 y ( n- 1)- y ( n- 2) + x ( n- 1)- 2 x ( n- 2) (a) Assume the recursion describe a system that is causal and relaxed. Is the system LTI? Find its impulse response sequence and verify whether it is BIBO stable or not. (b) Assume now that the initial conditions are y (- 2) = 0 and y (- 1) = 1 . Is the system LTI? Find its impulse response sequence....
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Homework_6 - 1 EE113 Homework 6 Problem 8.37 The input...

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