I'm not sure how to approach this problem. I will describe what I am trying to do, and what some of my matlab outputs look like. I'm not trained in signal processing or anything, so please be patient reading.
I have a fourier transform of some signal, and its frequency domain covariance matrix. For example, say my signal $x[f]$ is $100$ points long. Its covariance matrix $\Sigma$ is $100 \times 100$. I noticed that its diagonal is real, and when I plot it, it looks like a PSD. All the off diagonal elements are complex.
What I wish to do, is take the IFFT of the signal $x[f] \rightarrow x[t]$, and then plot $x[t]$ with error bars from the covariance $\Sigma$. Is this possible? After I take the IFFT of $x[f]$, what do I need to do to $\Sigma?$
Thank you for reading!