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MIT6_003S10_assn08

# MIT6_003S10_assn08 - 6.003 Homework 8 Please do the...

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± 6.003 Homework 8 Please do the following problems by Wednesday, April 7, 2010 . You need not submit your answers: they will NOT be graded. Solutions will be posted. Problems 1. Fourier Series Determine the Fourier series coeﬃcients for each of the following periodic CT signals. x 1 ( t )= x 1 ( t + 10) t 1 1 10 x 2 ( t )= x 2 ( t + 10) t 1 2 10 x 3 ( t )= x 3 ( t + 10) t 1 1 1 2 3 10 x 4 ( t )= x 4 ( t + 10) t 1 1 2 3 10 2. Inverse Fourier series Determine the CT signals with the following Fourier series coeﬃcients. Assume that the signals are periodic in T = 4. a. a k = î jk ; | k | < 3 0 otherwise b. b k = 1; k odd 0; k even

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± ² 2 6.003 Homework 8 / Spring 2010 3. Matching Consider the following sets of Fourier series coeﬃcients. 1 k a k 1 k b k = ³ 3 j 2 k k = ± 1 , ± 2 , ± 4 , ± 5 , ± 7 ,... 0 k = 0 , ± 3 , ± 6 , ··· 1 k c k 1 k d k 1 k e k 1 k f k a. Which (if any) set corresponds to the following periodic signal? 2
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MIT6_003S10_assn08 - 6.003 Homework 8 Please do the...

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