MIT6_003S10_assn05

MIT6_003S10_assn05 - 6.003 Homework 5 Due at the beginning...

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6.003 Homework 5 Problems 1. DT convolution Let y represent the DT signal that results when f is convolved with g , i.e., y [ n ] = ( f g )[ n ] which is sometimes written as y [ n ] = f [ n ] g [ n ]. Determine closed-form expressions for each of the following: y [ n ] f [ n ] g [ n ] y a [ n ] u [ n ] u [ n ] ( ) n ( ) n ( ) n ( ) n ( ) n 1 2 1 3 1 2 1 2 1 2 Due at the beginning of recitation on Wednesday, March 10, 2010 . y b [ n ] u [ n ] u [ n ] [ n ] u [ n ] u [ n ] y c y d [ n ] u [ n ] u [ n ] 2. CT convolution Let y represent the CT signal that results when f is convolved with g , i.e., y ( t ) = ( f g )( t ) which is sometimes written as y ( t ) = f ( t ) g ( t ). Determine closed-form expressions for each of the following: y ( t ) f ( t ) g ( t ) y a ( t ) u ( t ) u ( t ) y b ( t ) u ( t ) e t u ( t ) y c ( t ) e t u ( t ) e 2 t u ( t ) y d ( t ) e t u ( t ) e t u ( t )
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2 6.003 Homework 5 / Spring 2010 3. Convolutions Consider the convolution of two of the following signals. a ( t ) t 1 1 2 1 b ( t ) t 1 1 2 1 c ( t ) t 1 1 2 1 Determine if each of the following signals can be constructed by convolving ( a or b or c ) with ( a or b or c ). If it can, indicate which signals should be convolved. If it cannot, put an X in both boxes. Notice that there are ten possible answers: ( a a ), ( a b ), ( a c ), ( b a ), ( b b ), ( b c ), ( c a ), ( c b ), ( c c ), or (X,X). Notice also that the answer may not be unique. 1
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This note was uploaded on 12/14/2011 for the course EECS 6.003 taught by Professor Dennism.freeman during the Spring '11 term at MIT.

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MIT6_003S10_assn05 - 6.003 Homework 5 Due at the beginning...

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