test2_sol

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

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ) ....
View Full Document

## 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.

### Page1 / 4

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online