Quiz3_sol - EE3210 Signal and Systems Quiz 3 (Solution)...

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Unformatted text preview: EE3210 Signal and Systems Quiz 3 (Solution) Semester A, 2009/10 1. The answer is: ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎪ ⎨ ⎧ = − = − = − = = = otherwise 4 2 3 6 2 5 1 2 6 ] [ n n n n n n y 2. a) The signal is sketched below: 3 5 1 b) Let y ( t ) be the system’s response to x ( t ). [ ] ∫ ∫ ∞ − ∞ ∞ − − − − − − = − = 3 ) 5 ( ) 3 ( ) ( ) ( ) ( τ τ τ τ τ τ τ d t u t u e d t x h t y We can easily show that ) 5 ( ) 3 ( − − − − − τ τ t u t u is non-zero only in the range 3 5 − < < − t t τ . Therefore, for 3 ≤ t , we have y ( t ) = 0. For , we have 5 3 ≤ < t [ ] ) 3 ( 3 3 3 1 3 1 ) ( − − − − − = = ∫ t t e d e t y τ τ . For t > 5, we have [ ] [ ] 6 ) 5 ( 3 ) 3 ( 3 ) 5 ( 3 3 5 3 1 3 1 3 1 ) ( − − − − − − − − − − − = − = = ∫ e e e e d e t y t t t t t τ τ . 3. a) The difference equation is ] [ ] 2 [ 8 1 ] 1 [ 4 3 ] [ n x n y n y n y = − + − − . (4 marks) b) Construct the characteristic polynomial:...
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Quiz3_sol - EE3210 Signal and Systems Quiz 3 (Solution)...

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