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 2 3 1 4 j j + + A.2. 2 2 2 2 2 3 13 0.8745 17 1 4 Magnitude + = = + 1 1 3 4 tan tan 0.3430 19.65 340.45 2 1 Phase rad = ≈ − ≈ − ° ≈ ° Q.3. Find ( ) 0 sin lim x x x A.3. Using L’Hôpital’s Rule… ( ) ( ) [ ] ( ) 0 0 0 sin sin cos lim lim lim 1 1 x x x d x x x dx d x x dx = = = Using expansion of ( ) sin x ( ) 3 5 7 2 4 6 0 0 0 sin 3! 5! 7! lim lim lim 1 1 3! 5! 7! x x x x x x x x x x x x x + + = = + + = " " Q.4. Multiply 1 2 3 ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ and [ ] 4 5 6 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 [ ] ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) 1 1 4 1 5 1 6 4 5 6 2 4 5 6 2 4 2 5 2 6 8 10 12 3 3 4 3 5 3 6 12 15 18 ⎡ ⎤
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  • Spring '09
  • messner
  • lim, Partial fractions in complex analysis, 2 j, Daniel S. Brogan, 0.282 j, 0.3430 rad

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