Circular ARMA process

Let the circular ARMA process be defined by the AR recursion for intermediate sequence $ y_n$

$\displaystyle y_n = -\sum_{i=1}^P \; a_i \;y_{[n-i]_N} + e_n, \;\;\;\; 0\leq n \leq N-1$ (9.16)

followed by an MA recusion to generate $ x_n$:

$\displaystyle x_n = \sum_{i=0}^Q \; b_i \; y_{[n-i]_N}, \;\;\;\; 0\leq n \leq N-1$ (9.17)

where $ e_n$ are assumed to be $ N(0,\sigma^2)$ iid RVs and $ b_0=a_0=1$, and $ [n-i]_N$ means modulo-$ N$. The frequency-domain PDF for the circular ARMA process is given in (9.9)


Baggenstoss 2017-05-19