113_1_midterm_09_A

113_1_midterm_09_A - X z = ln(1 αz-1 | z |> | α |(b...

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EE113: Digital Signal Processing Prof. Mihaela van der Schaar Midterm Exam (Version A) Spring 2009 Name: Student ID: 1. A causal linear time-invariant system is initially relaxed and described by the difference equation y ( n ) - 5 y ( n - 1) + 6 y ( n - 2) = 2 x ( n - 1) (a) Determine the modes of the system. (b) Determine the impulse response of the system. (c) Determine the step response of the system using convolution. (d) Determine the step response of the system without using convolution. 2. (a) Consider the following complex series expansion of the natural logarithm for | t | < 1, ln(1 + t ) = X n =1 ( - 1) n +1 n t n , | t | < 1 Use the result to determine the sequence x ( n ) whose z-transform is given by
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Unformatted text preview: X ( z ) = ln(1 + αz-1 ) , | z | > | α | (b) Find the inverse z-transform of X ( z ) = z-1 1-( 1 2 ) 50 z-50 , | z | > 1 2 3. Consider the system illustrated in Figure 1. The output of an LTI system with an impulse response h ( n ) = ( 1 4 ) n u ( n +10) is multiplied by a unit step function u ( n ) to yield the output of the overall system. Answer each of the following questions, and briefly justify your answers: Figure 1: The overall system (a) Is the overall system linear? (b) Is the overall system time-invariant? (c) Is the overall system causal? (d) Is the overall system BIBO stable? 1...
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This note was uploaded on 06/01/2010 for the course EE EE113 taught by Professor Mihaela during the Spring '10 term at UCLA.

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