Question
Asked Mar 24, 2020
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Required information
Consider the following sequence of data
(x[0], x[1], x[2], x[3]) = (4,4,1,–2)
Without using a computer, find the forward DFT of the given sequence of data.
The values of the components of the forward DFT are X[0]
D. x[1) =
(Click to select) . X[2) =[
). and X[3] = (Cick to select)|
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Required information Consider the following sequence of data (x[0], x[1], x[2], x[3]) = (4,4,1,–2) Without using a computer, find the forward DFT of the given sequence of data. The values of the components of the forward DFT are X[0] D. x[1) = (Click to select) . X[2) =[ ). and X[3] = (Cick to select)|

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Expert Answer

Step 1

From the given data, the length of the sequence is 4.

Since, the DFT for the x(n) is expressed as:

Electrical Engineering homework question answer, step 1, image 1

Step 2

Substituting the known values in the above equation.

Hence, the DFT at the desired value can be evaluated using the above expression.

At, K=0:

Electrical Engineering homework question answer, step 2, image 1

Step 3

Similarly,

At, K=1:

Electrical Engineering homework question answer, step 3, image 1

...

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