Question

Using the DFT matrix, calculate the 4-point DFT of the signal $x[n] = \{1, 0, 2, 1\}$. Hence, show that the signal can be recovered by taking the 4-point inverse DFT.

          Using the DFT matrix, calculate the 4-point DFT of the signal
$x[n] = \{1, 0, 2, 1\}$.
Hence, show that the signal can be recovered by taking the 4-point inverse
DFT.

Added by Ricardo M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Amita Prajapat

Step 1

The DFT matrix for a 4-point DFT is given by: DFT = 1/sqrt(4) * [1 1 1 1; 1 -i -1 i; 1 -1 1 -1; 1 i -1 -i] To calculate the DFT of xn, we multiply the DFT matrix by xn: DFT(xn) = 1/sqrt(4) * [1 1 1 1; 1 -i -1 i; 1 -1 1 -1; 1 i -1 -i] * [1; 0; 2; 1] = Show more…

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Using the DFT matrix; calculate the 4-point DFT of the signal xn] {1,0,2,1}. Hence; show that the signal can be recovered by taking the 4 point inverse DFT