# Ringing/Oscillation in the reconstructed Periodogram

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

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

where $$p$$ is the AR model order

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 ?