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AnsClassEx2

# AnsClassEx2 - EE3118 Linear System and Signal Analysis Q1(a...

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EE3118 Linear System and Signal Analysis Answer of Class Exercise 2 Q1 (a) 2 0 π ω = (b) Consider the period from 0 to 4s, < < = 4 2 0 2 0 2 ) ( t t t t x ( ) [ ] [ ] n n n n n n t n n t n t dt t n t n t n dt t n t dt t n t x a ) 1 ( 1 ) ( 2 cos 1 ) ( 2 ) 5 . 0 ( ) 5 . 0 cos( 5 . 0 ) 5 . 0 sin( 2 1 0 ) 5 . 0 cos( 2 1 5 . 0 ) 5 . 0 sin( ) 5 . 0 cos( ) 2 ( 2 1 ) cos( ) ( 4 2 2 2 2 0 2 2 0 2 0 2 0 4 0 0 = = + = = = = π π π π π π π π π π π ω (c) If the frequency component is larger than 0.8 π , . 0 ) ( = ω H We only need to consider the d.c. term and the term with n=1. For n=1, or π ω 5 . 0 = , π ω ω 5 . 0 ) ( , 75 . 3 ) ( = = H H . Therefore, ) 5 . 0 5 . 0 sin( 5 . 7 ) 5 . 0 5 . 0 cos( 15 5 ) 5 . 0 5 . 0 sin( 75 . 3 2 ) 5 . 0 5 . 0 cos( 75 . 3 4 10 2 1 ) ( 2 2 π π π
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