Hãy xác định DFT của tín hiệu sau. x ˜ ( n ) = { 1 0 ≤ n ≤ 4 0 5 ≤ n ≤ 9

$\tilde{X}\left(k\right)=e{}^{-j\frac{2k\pi }{5}}$

$\tilde{X}\left(k\right)=\frac{\text{s}\text{i}\text{n}\frac{k\pi }{2}}{\text{s}\text{i}\text{n}\frac{k\pi }{10}}e{}^{-j\frac{2k\pi }{5}}$

$\tilde{X}\left(k\right)=e{}^{-jk\pi }$

$\tilde{X}\left(k\right)=5\cdot \frac{\text{s}\text{i}\text{n}\frac{k\pi }{2}}{\text{s}\text{i}\text{n}\frac{k\pi }{10}}e{}^{-j\frac{2k\pi }{5}}$