# How to Estimate a Normalized PSD Using the Burg’s Method in MATLAB?

I'll try to be most sintetic as I can. I'm using an EEG system and I want perform an frequency analisys of the brain waves. I found this interesting article which describe how is possible to discern the "like" or "dislike" statement of mind looking at some specific band frequencies. To do this, they calculate the Power Density Spectrum (PSD) usign the Burg method and then normalize it. Following the relative extract from article:

The power spectral density (PSD) of each epoch (16 epochs) for each subject (15 subjects) was estimated using the Burg method. The Burg method is an autoregressive (AR) pre-diction model based parametric spectral estimation method and yields a PSD estimate given by

$\widehat P(f)=\frac{1}{f_s}\frac{\epsilon_c}{|1+\sum_{k=1}^{c} \widehat a(k)e^{(2\pi jkf/f_s)}|}$

where fs is the sampling frequency, c is the order of the model, f is the frequency, and a(k) are the AR model parameters. These parameters are computed by the minimization of the back-ward and forward prediction errors while satisfying a specific recursion scheme called the Levinson–Durbin recursion. In the Burg method the signal whose PSD to be estimated is assumedto be the output of an all-pole linear system driven by whitenoise. In our study, the model order was taken as 15 after literature. This method estimates the model parameters directly without a need for the autocorrelation function calculation. The main advantages of this approach are resolving closely spaced sinusoids in signals with low noise levels, and successfully estimating power spectral densities of short data recordings. In addition, this technique guarantees a stable autoregressive model and is computationally efficient. For each epoch, we computed/estimated PSD values at each integer frequency. To be more specific, we have computed thespectrum at f = 4, 5, 6, . . ., 39, 40 Hz, total of 37 frequency points. We then normalized the power values using the sum of all power values in that segment to minimize inter-subject and intra-subject variability. Therefore, we obtained 37 normal-ized power values (NPVs) for each epoch (totally 16 epochs), [...]

Now I want recreate this analisys in MATLAB but I haven't deep knowledge of this method. I found only an specific function but I don't know how to use it to have the normalized values (NPV's) described above. I tried it but the I don't understand for example why the result band frequency is 0-129Hz. The lenght of my epochs is 1000 sample whit a sample frequency of 250Hz.

Maybe the answer to my question could be long and complicated but can anyone explain me how to use the MATLAB funcion correctly? Why in the article choose the Burg's method to obtain the PSD? And what means

We then normalized the power values using the sum of all power values in that segment

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