ecen314-fall11-hw4

# ecen314-fall11-hw4 - T B to the input y 1 ( t-τ ) ?...

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ECEN 314: Signals and Systems, Fall ‘11 Homework #4 Homework Assignment #4 Due date – Oct. 6, 2011 (Thu), 3:55PM in class. Problem 1. Block Diagram Representations (12 points) Draw the block diagrams for the causal LTI systems described by the following difference equations. [4 pt] (a) y [ n ] - 1 3 y [ n - 1] = 1 2 x [ n ] . [4 pt] (b) y [ n ] = 1 3 y [ n - 1] + 1 2 x [ n - 1] . [4 pt] (c) y [ n ] + 2 y [ n - 1] + 3 y [ n - 2] = 4 x [ n ] + 5 x [ n - 1] + 6 x [ n - 2] . Problem 2. Block Diagram Representations (12 points) Draw the block diagrams for the causal LTI systems described by the following differential equations. (Note: Do not use differentiators!) [4 pt] (a) y ( t ) + 1 2 d dt y ( t ) = 4 x ( t ) . [4 pt] (b) d dt y ( t ) + 3 y ( t ) = x ( t ) . [4 pt] (c) y ( t ) + 1 2 d dt y ( t ) + 1 3 d 2 dt 2 y ( t ) = x ( t ) + 2 d dt x ( t ) .

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Problem 3. Inverse System (8 points) Consider a LTI system T A , which has an inverse system T B . Let y k ( t ) be the output of the system T A when the input is x k ( t ) . [4 pt] (a) What is the response of system T B to the input ay 1 ( t ) + by 2 ( t ) , where a and b are constants? [4 pt] (b) What is the response of system
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Unformatted text preview: T B to the input y 1 ( t-τ ) ? Problem 4. Interconnected LTI systems (8 points) Consider three LTI systems: T 1 with an impulse response h 1 [ n ] , T 2 with h 2 [ n ] , and T 3 with h 3 [ n ] = h 2 [ n ] . Let h 2 [ n ] = u [ n ]-u [ n-2] . Suppose the three systems are connected in series, such that the input x [ n ] is ﬁrst passed through T 1 , then through T 2 , and ﬁnally through T 3 to get the ﬁnal output y [ n ] . [4 pt] (a) Let the overall response be h [ n ] = { 1 , 5 , 10 , 11 , 8 , 4 , 1 } , where the ﬁrst element corresponds to h [0] and the last corresponds to h [6] . Find the impulse response h 1 [ n ] of the system T 1 . [4 pt] (b) Find the response of the overall system to the input x [ n ] = δ [ n ]-δ [ n-1] ....
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## This note was uploaded on 01/01/2012 for the course ECEN 314 taught by Professor Halverson during the Fall '08 term at Texas A&M.

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ecen314-fall11-hw4 - T B to the input y 1 ( t-τ ) ?...

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