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30th May 2017, 11:49 #1
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30th May 2017, 11:49

31st May 2017, 10:51 #2
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Re: Fourier Transform Related Question
both options are incorrect.
x[n] = X(e^jw) not x[k]

31st May 2017, 10:51

31st May 2017, 16:27 #3
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Re: Fourier Transform Related Question
The definition of y[n] is not valid! if n = 1 y[n] = x[1/3]??? No! You probably have to specify that y[n] = x[n/3] for n = 3k, where k is and integer. This is called upsampling. In that case the second sum you wrote is correct. However, your parenthesis: e^jw(3k) is misleading! You should have written e^j(3w) k. You have to realize that X(e^jw) while standard, it a bit of an abuse of notation. Really the DTFT is a function of w. The sum you wrote is just the DTFT with 3w replacing w. Therefore we can do the same in X(e^jw) > X(e^3jw), number 2.
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31st May 2017, 16:27

31st May 2017, 23:36 #4
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Re: Fourier Transform Related Question
Small typo, you have to specify that y[n] = x[n/3] for n = 3k, where k is and integer AND 0 OTHERWISE.
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