Exam1F09

# Exam1F09 - EE538 Digital Signal Processing I Fall 2009 Exam...

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EE538 Digital Signal Processing I Fall 2009 Exam 1 Tuesday, Oct. 6, 2009 Cover Sheet Test Duration: 60 minutes. Coverage: Chapters 1-5. Open Book but Closed Notes. Calculators NOT allowed. This test contains two problems. All work should be done in blue books. You must show all work for each problem to receive full credit. Do not return the exam itself; just your blue book. Prob. No. Topic(s) Points 1. LTI Systems: Properties, 55 Transfer Functions, Frequency Response 2. DT Autocorrelation, Cross-Correlation 45 Correlation in terms of Convolution 1

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EE538 Digital Signal Processing I Exam 1 Fall 2009 Problem 1. [55 points] Consider a DT LTI system with the transfer function below, with a single pole at z = a , where a is real-valued and satisfies 0 < a < 1, and a single zero at z = 1 /a . Consider computing the frequency response of this system graphically. H ( z ) = ( z - 1 a ) ( z - a ) (1) (a) To this end, first find an expression for the length N ( ω ) of the vector that connects the zero at z = 1 /a to the point z = e on the unit circle, where 0 ω π .
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