Electrical Engineering 20N - Spring 2002 - Varaiya - Mid 2

# Electrical Engineering 20N - Spring 2002 - Varaiya - Mid 2...

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Unformatted text preview: EECS 20. Midterm No. 2 April 16, 2002. Please use these sheets for your answer and your work. Use the backs if necessary. Write clearly and put a box around your an- swer, and show your work. Print your name and lab TA’s name below Name: Lab TA: Problem 1: Problem 2: Problem 3: Problem 4: Total: 1 1. 30 points. Consider a continuous-time signal x : Reals → Reals defined by ∀ t ∈ Reals, x ( t ) = 3 + 2sin(3 t ) + 3cos(4 t ) . (a) Obtain the Fourier series coefficients of x ( t ) , i.e., find the coefficients A ,A 1 ,A 2 ,... and φ 1 ,φ 2 ,... and w such that x ( t ) = A + ∞ X k =1 A k cos( kw t + φ k ) . (b) Obtain the Fourier series expansion for x ( t ) , i.e., find the coefficients X k for all k ∈ Integers such that x ( t ) = ∞ X k =-∞ X k e ikw t . 2 (c) Consider a continuous-time LTI system Filter : [ Reals → Reals ] → [ Reals → Reals ] with the following frequency response: H ( w ) = 2 , | w | ≥ 2 , H ( w ) = 0 , | w | < 2 ....
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Electrical Engineering 20N - Spring 2002 - Varaiya - Mid 2...

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