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Let X(K) = {20, 0, -4+4j, 0, -4} is the 8 point DFT of a real valued sequence x(n)
  1. Find X(K) for K= 5, 6, 7. -
  2. Find the 8 point DFT P(K) such that - $p(n) = (-1)n \otimes x(n)$ Using DFT property. -
1 Answer
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  1. N=8

    For k=5, $X(5) = x*(8-5) \\ = x*(3) = 0$

    For k=6, $X(6) = x*(8-6) \\ = x*(2) = (-4-4j)$

    For k=7, $X(7) = x*(8-7) \\ = x*(1) = 0$

    $\therefore, X(5) = 0, X(6) = -4-4j, X(7) = 0$

    Result: X(K)={20, 0, -4+4j, 0, -4, 0, -4-4j, 0} …

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