If g(n) is a real valued sequence of 2N points and x1(n)=g(2n) and x2(n)=g(2n+1), then what is the value of G(k), k=0,1,2andhellip;N-1?a)X1(k)-W2kNX2(k)b)X1(k)+W2kNX2(k)c)X1(k)+W2kX2(k)d)X1(k)-W2kX2(k)Correct answer is option 'B'. Can you explain this answer? - EduRev Electrical Engineering (EE) Question

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If g(n) is a real valued sequence of 2N points and x1(n)=g(2n) and x2(n)=g(2n+1), then what is the value of G(k), k=0,1,2…N-1?

a)
X1(k)-W₂^kNX2(k)
b)
X1(k)+W₂^kNX2(k)
c)
X1(k)+W₂^kX2(k)
d)
X1(k)-W₂^kX2(k)

Correct answer is option 'B'. Can you explain this answer?

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If g(n) is a real valued sequence of 2N points and x1(n)=g(2n) and x2(...

Explanation: Given g(n) is a real valued 2N point sequence. The 2N point sequence is divided into two N point sequences x1(n) and x2(n)
Let x(n)= x1(n)+jx2(n)
=> X1(k)= 1/2 [X*(k)+X*(N-k)] and X2(k)= 1/2j [X*(k)-X*(N-k)] We know that g(n)= x1(n)+x2(n)
=>G(k)= X1(k)+W₂^kNX2(k), k=0,1,2…N-1.

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If g(n) is a real valued sequence of 2N points and x1(n)=g(2n) and x2(n)=g(2n+1), then what is the value of G(k), k=0,1,2…N-1?a)X1(k)-W2kNX2(k)b)X1(k)+W2kNX2(k)c)X1(k)+W2kX2(k)d)X1(k)-W2kX2(k)Correct answer is option 'B'. Can you explain this answer?

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