final_08 - Department of Electrical and Computer...

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Unformatted text preview: Department of Electrical and Computer Engineering The Johns Hopkins University 520.137 Introduction to Electrical and Computer Engineering – Fall 2008 Final Examination 1. There are 6 problems. You have 180 minutes . 2. Closed book. Closed notes. Three 8 . 5 × 11 cheat sheets allowed. 3. Read the questions carefully. Make sure that you answer every question posed. 4. Express your final answer in the most compact and simplified form. 5. Justify all of your answers. 6. State all of your assumptions if necessary. 7. Show your work clearly, neatly, and precisely. 8. Label all of your plots and sketches carefully. I Consider the mid-rise quantizer for a sinal x depicted in the figure below. x y D D 2 D 3 D- 2 D- –1 –2 1 2 … … x y D D 2 D 3 D- 2 D- –1 –2 1 2 … … (a) Find the mathematical expression describing the output of the quantizer y as a function of the input signal x . (5 points). (b) Find the set of reconstructed values { ˆ x i } using the centroid rule at the inverse quantizer. (10 points). (c) Find the mathematical expression describing the output of the inverse quantizer ˆ x i as a function of the quantized signal y . (5 points). (d) Sketch the quantization error signal q ( x ). (10 points)....
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This note was uploaded on 02/02/2010 for the course ENGINEERIN 520.101 taught by Professor Tracdtran during the Winter '06 term at Johns Hopkins.

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final_08 - Department of Electrical and Computer...

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