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Unformatted text preview: 1 t 1 x 1 ( t ) 6.003 Homework 9 Due at the beginning of recitation on Wednesday, April 14, 2010 . Problems 1. Fourier varieties a. Determine the Fourier series coeﬃcients of the following signal, which is periodic in T = 10. x 1 ( t ) t 1 − 1 − 3 − 10 1 3 10 b. Determine the Fourier transform of the following signal, which is zero outside the indicated range. x 2 ( t ) t 1 − 1 − 3 1 3 What is the relation between the answer to this part and that of the previous part? c. Determine the time waveform that corresponds to the following Fourier transform, which is zero outside the indicated range. X 3 ( jω ) ω 1 − 1 − 3 1 3 What is the relation between the answer to this part and that of the previous part? 2. Fourier transform properties Let X ( jω ) represent the Fourier transform of x ( t ) = e − t < t < 1 0 otherwise Express the Fourier Transforms of each of the following signals in terms of X ( jω ). Ø 6.003 Homework 9 / Spring 2010 2 1 1 − 1 t x 2 ( t ) 1 t 1 x 3 ( t ) 1 t 1 x 4 ( t ) 3. Fourier transforms Find the Fourier transforms of the following signals....
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 Spring '11
 DennisM.Freeman
 Fourier Series, FN, Fourier series coefficients

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