Practice Question on Computing the Fourier Transform of a Discrete-time Signal

Compute the Fourier transform of the signal

$ x[n] = u[n+1]-u[n-2].\ $

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Answer 1

$ \mathcal X (\omega) = \sum_{n=-\infty}^\infty (u[n+1]-u[n-2])e^{-j\omega n}=\sum_{n=-1}^2 e^{-j\omega n}= $

$ \mathcal X (\omega) = e^{j\omega}+1+e^{-j\omega}+e^{-j2\omega} $

--Cmcmican 19:57, 28 February 2011 (UTC)

TA's comments: You have a small mistake in that. Note that $ u[n-2] $ starts at $ n=2 $ and not $ n=3 $.

Answer 2

So it should be like this.

$ \mathcal X (\omega) = \sum_{n=-\infty}^\infty (u[n+1]-u[n-2])e^{-j\omega n}=\sum_{n=-1}^1 e^{-j\omega n}= $

$ \mathcal X (\omega) = e^{j\omega}+1+e^{-j\omega} $

--Cmcmican 11:57, 2 March 2011 (UTC)

Answer 3

Write it here.

Back to ECE301 Spring 2011 Prof. Boutin

Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang