Test2_sol - ECEN 314 Solution to Test#2 Georghiades Given December 8 2009 Instructions Exam is open-book open notes No calculators are allowed

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Unformatted text preview: ECEN 314 Solution to Test #2 Georghiades Given: December 8, 2009. Instructions : Exam is open-book, open notes. No calculators are allowed. Please give your solution in the allocated space. If more space is needed, use the back of the page. All problems carry equal weight. 1. Consider a linear, time-invariant system with transfer function H ( s ) = 1 ( s + 1) 2 . Compute the output y ( t ) of the system when the input signal x ( t ) = 2cos 2 ( t ) is applied and find its average energy over a period. Solution We can express x ( t ) using standard trigonometric identities as: x ( t ) = 2cos 2 ( t ) = 2 e jt + e- jt 2 ! 2 = 1 + 1 2 e j 2 t + 1 2 e- j 2 t The period of x ( t ) is T = π . Thus, the complex Fourier series coefficients of x ( t ) are x = 1, x 1 = 1 / 2 and x- 1 = 1 / 2. Then, y ( t ) = H (0) + 1 2 H ( j 2) e j 2 t + 1 2 H (- j 2) e- j 2 t = 1 + 1 2 e j 2 t (1 + j 2) 2 + 1 2 e- j 2 t (1- j 2) 2 = 1- 3 25 cos(2 t ) + 4 25 sin(2 t ) ....
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This note was uploaded on 01/01/2012 for the course ECEN 314 taught by Professor Halverson during the Spring '08 term at Texas A&M.

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Test2_sol - ECEN 314 Solution to Test#2 Georghiades Given December 8 2009 Instructions Exam is open-book open notes No calculators are allowed

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