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I have an original periodogram that I need to model with autoregressive process. However the model isn't right as it is not fitted well to the original periodogram.

I am suspecting I am doing something wrong when taking the IFFT.

  • Normalize the original periodogram $I(f)$ so that the (sum of the integral is 1 on the normalized frequency)
  • Create a $2N-1\times1$ two sided periodogram from $N$ samples of the normalized periodogram
  • Take the $\sqrt{I(f)}$ of the signal from the last step
  • Generate random phase values from [0,2pi] and multiply the signal point with the phasors from the phase
  • Perform IFFT (Scipy IFFT, 0 frequency content - positive side content - negative side content )
  • Autocorrelate the generated IFFT signal
  • Use Autocorrelation method to solve for the AR parameters
  • Finally fit the AR model and generate Periodogram

\begin{equation} I(f)= \frac{1}{|\hat{A}(f)|^2} = \frac{1}{|a[0] + a[1]e^{-j2\pi f_1} + a[2]e^{-j2\pi f_2} +....+ a[p]e^{-j2\pi f_p}|^2} \end{equation}

where $p$ is the AR model order

enter image description here

Sorry, I can't show the whole plot for a reason. I am only showing the end of positive side spectrum

what am I doing wrong ?

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