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ECE · Q30

Signal Processing

Engineering and GATE · ECE · question 30

Q30

The DFT of a vector [a b c d] is the vector [α β γ δ]. Consider the product \[ [ p\,q\,r\,s ] = [ a\,b\,c\,d ] [ array*20c a&b&c&d \\ d&a&b&c \\ c&d&a&b \\ b&c&d&a array ]\] The DFT of the vector [p q r s] is a scaled version of

The DFT of a vector [a b c d] is the vector [α β γ δ]. Consider the product
\left[ {p\,q\,r\,s} \right] = \left[ {a\,b\,c\,d} \right]\left[ {\begin{array}{*{20}{c}} a&b&c&d \\ d&a&b&c \\ c&d&a&b \\ b&c&d&a \end{array}} \right]
The DFT of the vector [p q r s] is a scaled version of
A.
2 β2 γ2 δ2]
Answer
B.
C.
[α + β β + δ δ + γ γ + α]
D.
[α β γ δ]

Answer: Option A

Solution

Answer: Option A
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