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hw07su09

# hw07su09 - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of...

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GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGINEERING ECE 2025 Summer 2009 Problem Set #7 Assigned: June 23, 2009 Due Date: July 6-7, 2009 Please check the T-square chat and announcements daily. All official course announcements will be posted there. ALL of the STARRED problems should be turned in for grading. PROBLEM 7.1 *: Determine the z -transforms of the following sequences. For each sequence, express your answer three different ways: (1) a sum of rational functions; (2) a ratio of polynomials in z - 1 ; and (3) a product of factors of the form (1 - az - 1 ). (a) x [ n ] = (0 . 7) n u [ n ] + ( - 0 . 7) n u [ n ]. (b) x [ n ] = 3(0 . 8) n cos(0 . 2 πn ) u [ n ]. PROBLEM 7.2 *: Consider a discrete time LTI system with the system function H ( z ) = 2 + 1 . 3 z - 2 - 4 . 9 z - 5 4 + 0 . 8 z - 3 - 0 . 1 z - 7 (a) Find the input/output equation that relates the output y [ n ] to an arbitrary input x [ n ]. (To be a causal system, this equation should have a y [ n ] by itself on the left hand side.) (b) Suppose we had a signal xx in Matlab that we wanted to pass through this system using a command of the form

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• Spring '08
• JUANG
• LTI system theory, Impulse response, Georgia Institute of Technology, input/output equation, discrete time LTI

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