Quiz2_sol - EE3210 Signal and Systems Quiz 2 (Solution) 1....

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EE3210 Signal and Systems Quiz 2 (Solution) Semester A, 2009/10 1. a) Let h p ( t ) be the impulse response. Then [ ] ) ( 1 ) ( ) ( ) ( 2 1 t u e t h t h t h t p + = + = . b) The response is [ ] ) 1 ( 1 ) 1 ( + t u e t . 2. a) Fundamental period = 8. b) x [ n ] can be rewritten as follows: [ ] ) 5 / 4 / ( ) 5 / 4 / ( 2 1 5 4 sin ππ + + = + n j n j e e j n . Hence, 10 / 3 5 / 1 2 1 2 π j j e j e a = = , 10 / 3 5 / 1 2 1 2 j j e j e a = = , and a k = 0 for other values of k . 3. Using convolution integral, we have [] () 1 6 3 2 6 6 2 6 1 ) ( 3 2 ) ( 2 ) ( ) ( ) ( 1 0 2 1 0 1 0 1 0 = + = + = + = = = t t d t d t d t x d t x h t y ττ τ 4. The answer is: = = = = = otherwise 0 3 1 2 1 1 4 0 6 ] [ n n n n n y
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5. a) The plot is shown below: 02 4 -4 -2 b) Its period is equal to 2. c) The Fourier series coefficients: 2 1 ) ( 2 1 1 1 0 = = dt e t a t jk k ω δ 6. a) The two signals can be sketched as follows: t π 2 - -2 0 1 x ( t ) t 2 - -2 0 1 y ( t )
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b) y ( t ) can be represented by Fourier series, because it is periodic.
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Quiz2_sol - EE3210 Signal and Systems Quiz 2 (Solution) 1....

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