Spectral Factorization of Polynomials using Cholesky

A simple method to spectral factorize rho. aa*+bqb* where a and b are polynomials into d.d* or reps.dn.dn* where reps is a constant.

This Is useful for optimal control or optimal filtering problems

Spectral factorization using Cholesky decomposition
dc.dc*=a.a.rho+b.b*.q
dcn is normalised spectral factor
Uses the Toeplitz matrix approach
T.J.Moir Dec 2019
we need two polynomials b/a as in ARMAX approach for control.
no delay is not included in b polynomial - important
let m be much greater than a or b polynomial lengths eg 12
note, if q=0 then a is returned as spectral-factor UNCHANGED (NOT its mirror image in the z-plane).

The Cholesky factorization routine used is Matlab's own one but here is a way of applying it to polynomial spectral factorization.