Practice+Exam+3_Sakai - Practice Exam#3 Fourier series and...

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Practice Exam #3 1 Practice Exam #3 Fourier series and transform Lessons 24-33 Some answers are derived using 1 st principles, others from tables or class notes. Unless specified, the solution methodology is your choice. WARNING: Not all problems have the same degree of difficulty.
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Practice Exam #3 2 Problem 1 X(t) R=1 C=1 y(t) a) If x(t) = 15 e -5t u(t), what is the Fourier transform of x(t) (i.e., X( ))? R=10k C=10 F b) What is H( )?
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Practice Exam #3 3 X(t) R=1 C=1 y(t) c) What is Y( )? R=10k C=10 F d) What is y(t)?
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Practice Exam #3 4 Problem 2 Given an at-rest linear system characterized by: H( ) = {1 for | | 1 r/s, 0 otherwise} and an input x(t) = |sin(t/2)| (full wave rectified sinewave) having a known trigonometric Fourier series representation (textook, back cover): Even symmetry – cosine series. 0 2 0 1 1 H( ) Ideal 0 phase lowpass filter ) cos( ) ( ; ; / ; nt n t x f T n 1 4 1 4 2 1 2 1 2 2 1 0 0 0 π π ω π π
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Practice Exam #3 5 Problem 2 a) What is the trigonometric Fourier series of the output signal y(t)?
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