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A $4 \times 4$ DFT matrix is given by

$\dfrac{1}{2} \begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & x & -1 & y \\ 1 & -1 & 1 & -1 \\ 1 & -j & -1 & j \end{bmatrix} \\ j^2 = -1$

Where the values of $x$ and $y$ are ______, _____ respectively.

  1. $1, -1$
  2. $-1,1$
  3. $-j,j$
  4. $j, -j$
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Ans. is 4

4 X4 DFT matrix Def

1/N     1      1        1          1

          1       w    w^2      w^3

          1    w^2   w^4      w^6

          1   w^3    w^6      w^9

In this ex.

    

1\2              1      1       1       1

                   1      x      -1       y

                   1    -1        1      -1

                  1     -j        -1       j

given that (j2= -1)

=> here   w=x

x^2=-1 and j^2=-1

i.e. x=j 

w^3=y

w^3=-j

i.e. y=-j

Answer:

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