fall 2004 EE 3120 test #1

# fall 2004 EE 3120 test #1 - Let y n be the amount of water...

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Name:_____________________________________ EE 3120 Test # 1 SSN:_______________________________________ Fall 2004 DO NOT WRITE ON THE BACK OF THESE PAGES, IT WILL NOT BE GRADED Important equations: ( 1) 0 1 1 i n i i a a a + = - = - 1. Given the following input output pair, determine the output for a different input. The system is linear, and time-invariant. 2. A linear system is found to be time-varying. Given the following two input output pairs, select from the inputs which ones can we predict the output. Explain why you chose the input you did. 3. A discrete time LTI system has an impulse response given by: 1 [ ] [ ] [ 1] 3 n h n n u n δ = + - a. Plot h [ n ] b. Write h [ n ] in a more simplified form. c. Is the system causal? Explain d. What is the energy E x of h [ n ]? 4. Find the difference equation for the following signal flow graph. 5. Find the impulse response for the following difference equation. 6. Due to the fact that the city of New Orleans lies below sea level and sits inside a bowl created by the levies surrounding it, it has to pump out any rain that falls into the city.
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Unformatted text preview: Let y [ n ] be the amount of water on the ground at hour n. Let x [ n ] be the amount of rain that enters the city hour n . Let p [ n ] be the amount of water pumped out of the city in hour n . In theory, the pumping system can pump out 2 inches of rain every hour. Let’s assume that the pumps can pump out 2 inches the first hour, but the capacity to pump decreases by 2 % each hour due to the pumps heating and wearing down. In other words p [ n ] = .98 p [ n-1] a. Write a difference equation to describe how much water is on the ground at hour n . b. A fictitious hurricane “Tom” begins (at hour 0) to bring 3.5 inches of rain every hour, and also pushes 1 inch of flood water over the levy into the city every hour. An individual goes to bed at 10pm, and the hurricane hits at 11pm. His job is closed due to the expecting hurricane, so he sleeps in until 8am. How much water is on the ground when he wakes up?...
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