AnsClassEx1 - ) ( 9 ) ( 4 ) ( t y dt t dy dt t dx + = ....

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EE3118 Linear Systems and Signal Analysis Class Exercise 1 (30 minutes) Name: _____________________________ Student I.D.: ____________________ Q1. (a) Express the following signal x(t) in terms step function u(t) and ramp function r(t) only. [3 marks] (b) Consider a linear and time invariant system H , and it is known that its output is ( 29 t y S and ( 29 t y R if a unit step and a unit ramp signals are inputted, respectively. What is the output of the system if the signal x(t) in Q1(a) is inputted? [3 marks] Q2. Sketch the function: ( 29 t u t r t h - - = 6 ) 4 ( 3 ) ( [3 marks] Q3. The impulse response of a system is given as ) ( ) ( t u e t h t × = - . Using the convolution integral to determine the output if the input is ) ( ) ( t u t t x × = . [7 marks] [ ] [ ] 1 ) ( ) ( ) ( ) ( ) ( 0 0 0 0 0 ) ( - + = - = - = = = - = = - - - - - - - - t t t t t t t t t t t e t e t d e e de d e d t h x t h t x t y t t t t t t t t t t t t t x(t)=2r(t-5)-2r(t-15)-20u(t-20) Output y(t)=2 ( 29 5 - t y R -2 ( 29 15 - t y R -20 ( 29 20 - t y S 4 6 6 t h(t)
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Q4. Given that a system is governed by the following ordinary differential equation:
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Unformatted text preview: ) ( 9 ) ( 4 ) ( t y dt t dy dt t dx + = . Derive the steady state output response y(t) if a sinusoidal input ) 3 sin( 2 ) ( t t x = is applied. [9 marks] Let t j e t x 3 2 ) ( = and ) 3 ( ) ( q + = t j Be t y Since ) ( 9 ) ( 4 ) ( t y dt t dy dt t dx + = , we have )] 3 / 4 ( tan 2 / [ ) 3 / 4 ( tan 2 / ) 3 ( ) 3 ( 3 1 1 4 . 5 2 3 4 2 9 12 6 9 12 6 9 ) 3 ( 4 ) 3 ( 2----+ + = = + = + = + = + = p p q q q q q j j j j j j t j t j t j e e e j j j j Be Be Bje j Be e j B e j Hence, 4 . = B and 6435 . 3 4 tan 2 1 =      -=-p q Take the imaginary part, we have ) 6435 . 3 sin( 4 . ) ( + = t t y [ Note: q j e b a jb a-+ = + 2 2 1 1 where       =-a b 1 tan q ]...
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This note was uploaded on 01/11/2011 for the course EE 3118 taught by Professor Kitsangtsang during the Spring '08 term at City University of Hong Kong.

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AnsClassEx1 - ) ( 9 ) ( 4 ) ( t y dt t dy dt t dx + = ....

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