Two sequences [a, b, c] and [A, B, C] are related as,
\[\left[ {\begin{array}{*{20}{c}}
A \\
B \\
C
\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
1&1&1 \\
1&{W_3^{ - 1}}&{W_3^{ - 2}} \\
1&{W_3^{ - 2}}&{W_3^{ - 4}}
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
a \\
b \\
c
\end{array}} \right]\] where, $${W_3} = {e^{i\frac{{2\pi }}{3}}}.$$
If another sequence [p, q, r] is derived as,
\[\left[ {\begin{array}{*{20}{c}}
a \\
b \\
c
\end{array}} \right] = \] \[\left[ {\begin{array}{*{20}{c}}
1&1&1 \\
1&{W_3^1}&{W_3^2} \\
1&{W_3^2}&{W_3^4}
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
1&0&0 \\
0&{W_3^2}&0 \\
0&0&{W_3^4}
\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
{A/3} \\
{B/3} \\
{C/3}
\end{array}} \right]\]
then the relationship between the sequences [p, q, r] and [a, b, c] is
A. [p, q, r] = [b, a, c]
B. [p, q, r] = [b, c, a]
C. [p, q, r] = [c, a, b]
D. [p, q, r] = [c, b, a]
Answer: Option C
This Question Belongs to Electronics And Communications Engineering >> Signal Processing
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