Note that of a real process is a function of . Therefore, is a function of Consider rational spectrum so that where and are polynomials in . If is a root of so is Thus the roots of are symmetrical about the unit circle groups the poles and zeros inside the unit circle and
groups the poles and zeros outside the unit circle.
can be factorized into a minimum-phase and a maximum-phase factors
i.e.
and
In general spectral factorization is difficult, however for a signal with rational power spectrum, spectral factorization can be easily done.
of a real process is a function of 
. Therefore, 
is a function of
Consider rational spectrum 
where 
and 
are polynomials in 
. If 
Thus the roots of 
groups the poles and zeros inside the unit circle and 
and 