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Unformatted text preview: 6.003 Homework 2 Due at the beginning of recitation on Wednesday, September 23, 2009 . Problems 1. Characterizing block diagrams Consider the system defined by the following block diagram: Delay Delay Delay + + + 3 2 1 2 X Y a. Determine the system functional H = Y X . b. Determine the poles of the system. c. Determine the unit-sample response of the system. Express your answer as a sum of fundamental modes. 2. Finding a system a. Determine the difference equation and block diagram representations for a system whose output is 10 , 1 , 1 , 1 , 1 ,... when the input is 1 , 1 , 1 , 1 , 1 ,... . b. Determine the difference equation and block diagram representations for a system whose output is 1 , 1 , 1 , 1 , 1 ,... when the input is 10 , 1 , 1 , 1 , 1 ,... . c. Compare the difference equations in parts a and b. Compare the block diagrams in parts a and b. 3. Oscillations Let y [ n ] represent a discrete cosine wave, y [ n ] = cos n. Determine the coefficients of a difference equation for y of the form y [ n ] = a 1 y [ n 1] + a 2 y [ n 2] + ....
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- Spring '11