AR circular power spectral model

Circular AR models are just a simplification of the circular ARMA models discussed in Section 10.1.6, with $Q=0$. An order-$P$ auto-regressive (AR) process is defined by the innovation variance $\sigma^2$ and the AR coefficients $a_1, \; a_2 \ldots a_P$. The circular power spectrum of a circular AR process is given by

$$\rho_k = \frac{\sigma^2}{\vert A_k\vert^2},$$ (11.4)

where $\{A_k\}$, is the DFT of the AR parameters zero-padded to length $N$: ${\rm DFT}([1, -a_1, -a_2 \ldots -a_P, 0 , 0\ldots])$.