GATE Electronics and Communications (EC) 2015 Shift 1 Solved Paper

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Question : 53 of 65

Marks: +1, -0

Two sequences

[a,\:b,\:c\:and\: [.A,\:B,\:C]

are related as,

{[\table A ; B ; C]}={[\table 1 , 1 , 1 ; 1 , w_3^{-1} , w_3^{-2} ; 1 , w_3^{-2} , w_3^{-4}]}{[\table a ; b ; c]}

where

w_3=e^{ {\j} \;{2 π}/{3}}

If another sequence

p,q,\:r

is derived as,

{[\table {\p} ; {\q} ; {\r}]}={[\table 1 , 1 , 1 ; 1 , {\w}_3^1 , {\w}_3^2 ; 1 , {\w}_3^2 , {\w}_3^4]}{[\table 1 , 0 , 0 ; 0 , {\w}_3^2 , 0 ; 0 , 0 , {\w}_3^4]}{[\table \;{ {\A}}/{3} ; \;{ {\B}}/{3} ; \;{ {\C}}/{3}]}

Then the relationship between the sequences

[p,\:q,\:r\:and\: [.a,\:b,\:c] \:is

$[p,q,r] = [b,a,c]$
$[p,q,r] = [b,c,a]$
$[p,q,r] = [c,a,b]$
$[p,q,r] = [c,b,a]$

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