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# test1 - ECE 301 Sum 2010 Test 1 with Answers 1 1 An IIR...

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ECE 301 - Sum 2010 Test 1 with Answers 1 1. An IIR filter, having zero initial conditions, is defined by the following difference equa- tion: y m 1 1 y m 1 0 7 y m 2 5 x m . The input is x m 2 δ m 1 δ m 3 . Compute and plot y m for 0 m 4. ANS: y m m 3 m 0 0 10 11 0 1 7 6 See Detailed Solution to Prob. 1-9 for method. 2. An analog filter, with input voltage x t and output voltage y t , is defined by the ODE d dt y t 5 000 y t 10 000 x t The Backward Difference method (i.e., backward Euler’s method, backward derivative approxi- mation) with T s 50 μ sec is used to find the difference equation implementing the digital filter. The difference equation can be written as y m A y m 1 B x m . Compute A and B . ANS: A 0 8 B 0 4 See Detailed Solution to Prob. 2-4 for method. 3. A signal g m has the form g m 2 0 8 m u m 0 4 m u m . Compute the z -transform G z . Express your answer by writing G z in a factored form in which the poles and zeros are evident by inspection.

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