# hw10 - 6.003 Homework 10 Please do the following problems...

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6.003 Homework 10 Please do the following problems by Wednesday, November 18, 2009 . You need not submit your answers: they will NOT be graded. Solutions will be posted. 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 ( ) 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 ( ) represent the Fourier transform of x ( t ) = ± e t 0 < t < 1 0 otherwise Express the Fourier Transforms of each of the following signals in terms of X ( ). 1 t 1 x 1 ( t )

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6.003 Homework 10 / Fall 2009 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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## This note was uploaded on 08/24/2011 for the course EECS 6.003 taught by Professor Dennism.freeman during the Spring '11 term at MIT.

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hw10 - 6.003 Homework 10 Please do the following problems...

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