Convert normalized frequency to real frequency in AR model

Question

Let us suppose that we have modeled signal using AR model, and suppose we have following model:

I used spectral estimation function from MATLAB

pyulear

Now frequencies are given in normalized frequencies and I would like to know how to convert them back to real frequencies? From there it is clear that we have four deterministic model and also plus some white noise, actually I want to know approximate frequencies in each deterministic model. I can of course determine this frequencies using FFT, periodogram and so on, but I am studying application of the AR/ARMA model. So in my case, I have such frequencies on following figures, how can I determine actual frequencies? Thanks in advance.

Answer 1

Matlab generally uses normalized frequencies in radians/sample. If the signal is real-valued then these frequencies are in the interval $[0,\pi]$ (as you can see in the plot). The Matlab frequency variable $w$ is normalized as

$$w=\frac{2\pi f}{f_s}$$

where $f_s$ is the sampling frequency. So $w=\pi$ corresponds to $f=f_s/2$.