Converting PSD to Time Domain Signal
@Amelia. Hi. I tried to run your MATLAB code, but it contains several errors regarding vector lengths and produces error messages. But that's not the main issue here. The answer to your question is: If you compute the DFT of an N-point x(n) sequence you produce an N-point complex-valued xDFT(m) frequency-domain sequence. You can only reconstruct the original x(n) sequence by computing the inverse DFT of the N-point xDFT(m) sequence. You cannot recover the original N-point x(n) sequence by computing the inverse DFT of any sequence that is not the xDFT(m) sequence.