UGC NET CSE | November 2017 | Part 3 | Question: 64

Question

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.

• A. $1, -1$
• B. $-1,1$
• C. $-j,j$
• D. $j, -j$

Answer 1

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