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Let $x(n)=\sin (2 \pi k n / N), n=0,1, \ldots, N-1$, where $2 k \neq N$ and $0<k \leq N-1$. Then the circular convolution of $\{x(n)\}$ with itself is

  1. $N \cos (4 \pi k n / N)$
  2. $N \sin (4 \pi k n / N)$
  3. $-N \cos (2 \pi k n / N) / 2$
  4. $-N \sin (2 \pi k n / N) / 2$
  5. None of the above
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