AR circular power spectral model

Circular AR models are just a simplification of the circular ARMA models discussed in Section 9.1.6, 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

$\displaystyle \rho_k = \frac{\sigma^2}{\vert A_k\vert^2},$ (10.4)

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])$.

Baggenstoss 2017-05-19