hãy xác định công thức đúng của biến đổi fourier rời rạc (DFT) với dãy có chiều dài hữu hạn.

$X(k){}_N=\{\begin{array}{c}\sum {}_{n=0}^{N-1}\mathrm{Unsupported\; }x\left(n\right)\text{W}{}_{\text{N}}^{\text{k}\text{n}}\\ 0\le k\le N-1\\ 0\\ k\text{c}\text{ò}\text{n}\text{l}\text{a}\text{i}\end{array}$

$X(k){}_N=\{\begin{array}{c}\sum {}_{n=\infty }^{\infty }\mathrm{Unsupported\; }x\left(n\right)\text{W}{}_{\text{N}}^{\text{k}\text{n}}\\ 0\le k\le N-1\\ 0\\ k\text{c}\text{ò}\text{n}\text{l}\text{a}\text{i}\end{array}$

$X(k){}_N=\{\begin{array}{c}\sum {}_{n=0}^{N-1}\mathrm{Unsupported\; }x\left(n\right)\text{W}{}_{\text{N}}^{\text{k}\text{n}}\\ -\infty \le k\le \infty \\ 0\\ k\text{c}\text{ò}\text{n}\text{l}\text{a}\text{i}\end{array}$

$X(k){}_N=\{\begin{array}{c}\sum {}_{n\to \infty }^{\infty }\mathrm{Unsupported\; }x\left(n\right)\text{W}{}_{\text{N}}^{\text{k}\text{n}}\\ -\infty \le k\le \infty \\ 0\\ k\text{c}\text{ò}\text{n}\text{l}\text{a}\text{i}\end{array}$