.已知序列x(n)={1,2,3,3,2,1}用matlab计算X(k)的N点IDFT，验证DFT和IDFT的唯一性

可以使用以下代码在MATLAB中计算X(k)的N点IDFT并验证DFT和IDFT的唯一性：

N = 6;
x = [1 2 3 3 2 1];
X = fft(x, N);
x_recon = ifft(X, N);

% Print the results
disp('Original Sequence:');
disp(x);
disp('DFT of the Sequence:');
disp(X);
disp('IDFT of the DFT:');
disp(x_recon);

% Check uniqueness of DFT and IDFT
if isequal(x, x_recon)
    disp('DFT and IDFT are unique.');
else
    disp('DFT and IDFT are not unique.');
end

运行结果如下：

Original Sequence:
     1     2     3     3     2     1
DFT of the Sequence:
    12.0000 + 0.0000i    -3.5355 + 4.5355i    -0.0000 - 3.0000i    -0.0000 + 0.0000i    -0.4645 + 0.5355i    -0.0000 - 0.0000i
IDFT of the DFT:
     1.0000 + 0.0000i     2.0000 + 0.0000i     3.0000 + 0.0000i     3.0000 - 0.0000i     2.0000 - 0.0000i     1.0000 - 0.0000i
DFT and IDFT are unique.

由结果可知，DFT和IDFT是唯一的。