Question #2 Obtain the DFT of a discrete time signal given as x[n] = 2rect(n – 2) a) By using the direct DFT formula (i.e., the summation formula given into your lecture notes). b) By using matrix-vector expression of DFT (i.e., determine the transformation matrix then obtain the DFT of the given signal via this matrix). Hint: As you can see from its structure the above signal has 3 samples. So, you have to construct a 3 x 3 transformation matrix for item (b).

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Question #2
Obtain the DFT of a discrete time signal given as
x[n] = 2rect(n – 2)
a)
By using the direct DFT formula (i.e., the summation formula given into your lecture notes).
b)
By using matrix-vector expression of DFT (i.e., determine the transformation matrix then obtain
the DFT of the given signal via this matrix).
Hint: As you can see from its structure the above signal has 3 samples. So, you have to construct a 3 x 3
transformation matrix for item (b).
c)
By using its DTFT.
Hint: Please remember that you can obtain DFT of a signal by utilizing uniform sampling onto its DTFT.
Transcribed Image Text:Question #2 Obtain the DFT of a discrete time signal given as x[n] = 2rect(n – 2) a) By using the direct DFT formula (i.e., the summation formula given into your lecture notes). b) By using matrix-vector expression of DFT (i.e., determine the transformation matrix then obtain the DFT of the given signal via this matrix). Hint: As you can see from its structure the above signal has 3 samples. So, you have to construct a 3 x 3 transformation matrix for item (b). c) By using its DTFT. Hint: Please remember that you can obtain DFT of a signal by utilizing uniform sampling onto its DTFT.
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