ECE634S09_L1_ReviewQuiz

ECE634S09_L1_ReviewQuiz - ECE634 Signals and Systems II...

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ECE634 Signals and Systems II, Spring 2009 - Lecture 1, January 21 Daniel S. Brogan 1 Background knowledge quiz problems with solutions: Q.1. Express 3 2 j e in rectangular coordinates. A.1. Using Euler’s identity: () ( ) 2cos 3 2 sin 3 1.980 0.282 j j +≈ + Q.2. Find the magnitude and phase of 23 14 j j + + A.2. 22 1 3 0.8745 17 Magnitude + == + 11 34 tan tan 0.3430 19.65 340.45 21 Phase rad −− ⎛⎞ =−≈ ° ° ⎜⎟ ⎝⎠ Q.3. Find () 0 sin lim x x x A.3. Using L’Hôpital’s Rule… [] 00 0 sin sin cos lim lim lim 1 1 xx x d x dx d x x dx →→ ⎡⎤ ⎣⎦ = Using expansion of sin x 357 246 0 sin 3! 5! 7! lim lim lim 1 1 3! 5! x xxx x x −+−+ + + = " " Q.4. Multiply 1 2 3 ⎢⎥ and [ ] 456 in two orders A.4. () () 1 4 5 6 2 4 1 5 2 6 3 4 10 18 32 3 =++= + + =
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ECE634 Signals and Systems II, Spring 2009 - Lecture 1, January 21 Daniel S. Brogan 2 [] () ( ) () () ()( ) () () 11 4 1 5 1 6 4 5 6 2456 24 25 26 81 01 2 33 4 3 5 3 6 1 2 1 5 1 8 ⎡⎤ ⎢⎥ == ⎣⎦ Q.5. Use partial fraction expansion on ( ) 3 12 s ss s + + + A.5. This is one of several possible methods, and often one of the simplest: ( ) 3 1 2 sA B C s s s s + =+ + ++ + + Multiplying both sides by s
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ECE634S09_L1_ReviewQuiz - ECE634 Signals and Systems II...

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