hw01-3723-06f - ) ( ) ( 5 [ ) 1 ( , e) dt t e t j ) 3 2 ( ,...

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ECEN/MAE 3723 Systems I Fall 2006 Homework Assignment #1 Problem 1 : Make labeled sketches of the following time signals, based on a given continuous time signal, ) ( t x , shown on the right: a) ) ( 5 . 0 t x , b) 1 ) 2 ( + t x , c) ) 2 ( t x , d) ) 1 ( t x , e) ) 1 2 ( 5 . 0 ) 3 3 ( + t x t x . Problem 2 : Exercise the algebra and express the signal et x t y t () () () = in the form of ) sin( ϕ ω + t A where ) 20 cos( 5 ) ( ) 20 sin( 3 ) ( o o = + = t t y t t x . Find the parameters A and . Problem 3 : Evaluate the following integrals involving the impulse function: a) () + dt t t t t sin ) 1 ( cos ) ( δ , b) () + + dt t t e t u t ) 1 ( ) 1 ( ) ( , c) dt t e t j ) 1 2 ( , d) + + dt t t t e t t )] ( 5 cos
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Unformatted text preview: ) ( ) ( 5 [ ) 1 ( , e) dt t e t j ) 3 2 ( , f) d t u e t )) 3 ( ) sin( ) 1 ( ) ( ( 2 2 + . Problem 4 : Express the following signals, ) ( ), ( ), ( 3 2 1 t x t x t x in terms of unit ramp functions. Problem 5 :Describe the periodic signal, ) ( t x , shown below (the signal x ( t ) has only three periods). Problem 6 :Express the signal ) ( t x in terms of some basic functions....
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hw01-3723-06f - ) ( ) ( 5 [ ) 1 ( , e) dt t e t j ) 3 2 ( ,...

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